LATIN SQUARES. New Developments in the Theory and Applications
|
|
- Gladys Barnett
- 6 years ago
- Views:
Transcription
1 LATIN SQUARES New Developments in the Theory and Applications J. DENES Industrial and Scientific Consultant Formerly Head of Mathematics Institute for Research and Co-ordination of Computing Techniques (SZKI) Budapest, Hungary and A.D. KEEDWELL Department of Mathematical and Computing Sciences University of Surrey Guildford, United Kingdom With specialist contributions by G.B. BELYAVSKAYA A.E. BROUWER T. EVANS K. HEINRICH C.C. LINDNER D.A. PREECE 1991 NORTH-HOLLAND - AMSTERDAM NEW YORK OXFORD TOKYO
2 Vll CONTENTS Preface Acknowledgements xi xiii CHAPTER 1. INTRODUCTION. (J. Denes and A. D. Keedwell) (1) Basic definitions. 1 (2) Orthogonal latin squares. 2 (3) Isotopy and parastrophy. 4 CHAPTER 2. TRANSVERSALS AND COMPLETE MAPPINGS. (J. De'nes and A. D. Keedwell) (1) Basic facts and definitions. 7 (2) Partial transversals. 9 (3) Number of transversals in a latin square. 14 (4) Sets of mutually orthogonal latin squares with no common transversal. 23 (5) Sets of mutually orthogonal latin squares which are not extendible. 28 (6) Generalizations of the concepts of transversal and complete mapping. 33 ADDITIONAL REMARKS. 3 9 CHAPTER 3. SEQUENCEABLE AND R-SEQUENCEABLE GROUPS: ROW COMPLETE LATIN SQUARES. (J. De'nes and A. D. Keedwell) (1) Row-complete latin squares and sequenceable groups. 43 (2) Quasi-complete latin squares, terraces and quasisequenceable groups. 58 (3) R-sequenceable and R h -sequenceable groups. 67 (4) Super P-groups. 75 (5) Tuscan squares and a graph decomposition problem. 79 (6) More results on the sequencing and 2-sequencing of groups. 84 ADDITIONAL REMARKS. 99
3 Vlll Contents CHAPTER 4. LATIN SQUARES WITH AND WITHOUT SUBSQUARES OF PRESCRIBED TYPE. (K. Heinrich) 101 (1) Introduction. 102 (2) Without subsquares. 113 (3) With subsquares. 119 (4) With subsquares and orthogonal. 133 (5) Acknowledgement. 147 ADDITIONAL REMARKS BY THE EDITORS. 147 CHAPTER 5. RECURSIVE CONSTRUCTIONS OF MUTUALLY ORTHOGONAL LATIN SQUARES. (A. E. Brouwer) 149 (1) Introductory definitions. 150 (2) Pairwise balanced designs - definitions. 151 (3) Simple constructions for transversal designs. 152 (3)* Examples. 156 (4) Wilson's construction. 159 (4)* Examples. 161 (5) Weighting and holes. 162 (5)* Examples. 164 (6) Asymptotic results. 165 (7) Table of values of N(v) up to v= ADDITIONAL REMARKS BY THE EDITORS. 166 CHAPTER 6. r-orthogonal LATIN SQUARES. (G. B. Belyavskaya) (1) Some weaker modifications of the concept of orthogonality. 169 (2) r-orthogonal latin squares and quasigroups. 171 (3) Partial admissibility of quasigroups, its connection with r-orthogonality. 177 (4) Spectra of partial orthogonality of latin squares (quasigroups). 186 (5) Near-orthogonal and perpendicular latin squares. 190 (6) r-orthogonal sets of latin squares. 195 (7) Applications of r-orthogonal latin squares and problems raised thereby. 200 CHAPTER 7. LATIN SQUARES AND UNIVERSAL ALGEBRA. (T. Evans) 203 (1) Universal algebra preliminaries. 204 (2) Varieties of latin squares. 206
4 Contents ix (3) Varieties of orthogonal latin squares. 208 (4) Euler's conjecture. 211 (5) Free algebras and orthogonal latin squares. 212 CHAPTER 8. EMBEDDING THEOREMS FOR PARTIAL LATIN SQUARES. (С. С Lindner) 217 (1) Introduction. 218 (2) Systems of distinct representatives. 219 (3) The theorems of Ryser and Evans (on latin rectangles and squares). 222 (4) Cruse's theorems (on commutative latin rectangles and squares). 225 (5) Embedding idempotent latin squares. 229 (6) Conjugate quasigroups and identities. 236 (7) Embedding semisymmetric and totally symmetric quasigroups. 240 (8) Embedding Mendelsohn and Steiner triple systems. 243 (9) Summary of embedding theorems. 253 (10) The Evans' conjecture. (Smetaniuk's proof.) 254 APPENDIX (1). Alternative description of Smetaniuk's proof of the Evans' conjecture. 261 APPENDIX (2). Additional Bibliography. 265 CHAPTER 9. LATIN SQUARES AND CODES. (J. De'nes and A. D. Keedwell) 267 (1) Basic facts about error-detecting and correcting codes. 268 (2) Codes based on orthogonal latin squares and their generalizations. 272 (3) Row and column complete latin squares in coding theory. 283 (4) Two-dimensional coding problems. 290 (5) Secret-sharing systems. 303 (6) Miscellaneous results. 308 ADDITIONAL REMARKS. 314 CHAPTER 10. LATIN SQUARES AS EXPERIMENTAL DESIGNS. (D. A. Preece) (1) Introduction. 317 (2) The design and and analysis of experiments.. 318
5 X Contents (3) Some practical examples of latin squares used as row-andcolumn designs. 322 (4) Some other uses of latin squares in experimental design. 324 (5) The use of latin squares in experiments with changing treatments. 327 (6) Other "latin" experimental designs. 329 (7) Statistical analysis of latin square designs. 331 (8) Randomization of latin square designs. 338 (9) Polycross designs. 341 CHAPTER 11. LATIN SQUARES AND GEOMETRY. (J. Denes and A. D. Keedwell) (1) Complete sets of mutually orthogonal latin squares and projective planes. 343 (2) Projective planes of orders 9, 10, 12 and (3) Non-desarguesian projective planes of prime order. 351 (4) Digraph complete sets of latin squares and incidence matrices. 352 (5) Complete sets of column orthogonal latin squares and affine planes. 358 (6) The Paige-Wexler latin squares. 360 (7) Miscellanea. 373 ADDENDUM. 377 CHAPTER 12. FREQUENCY SQUARES. (J. De'nes and A. D. Keedwell) (1) F-squares and orthogonal F-squares. 381 (2) Enumeration and classification of F-squares. 388 (3) Completion of partial F-squares (4) F-rectangles and other generalizations. 392 (5) A generalized Bose construction for orthogonal F-squares. 396 ADDITIONAL REMARKS. 398 Bibliography 399 Subject Index 444
How Many Mates Can a Latin Square Have?
How Many Mates Can a Latin Square Have? Megan Bryant mrlebla@g.clemson.edu Roger Garcia garcroge@kean.edu James Figler figler@live.marshall.edu Yudhishthir Singh ysingh@crimson.ua.edu Marshall University
More informationThe number of mates of latin squares of sizes 7 and 8
The number of mates of latin squares of sizes 7 and 8 Megan Bryant James Figler Roger Garcia Carl Mummert Yudishthisir Singh Working draft not for distribution December 17, 2012 Abstract We study the number
More informationGraduate Texts in Mathematics. Editorial Board. F. W. Gehring P. R. Halmos Managing Editor. c. C. Moore
Graduate Texts in Mathematics 49 Editorial Board F. W. Gehring P. R. Halmos Managing Editor c. C. Moore K. W. Gruenberg A.J. Weir Linear Geometry 2nd Edition Springer Science+Business Media, LLC K. W.
More informationSudoku an alternative history
Sudoku an alternative history Peter J. Cameron p.j.cameron@qmul.ac.uk Talk to the Archimedeans, February 2007 Sudoku There s no mathematics involved. Use logic and reasoning to solve the puzzle. Instructions
More informationLatin squares and related combinatorial designs. Leonard Soicher Queen Mary, University of London July 2013
Latin squares and related combinatorial designs Leonard Soicher Queen Mary, University of London July 2013 Many of you are familiar with Sudoku puzzles. Here is Sudoku #043 (Medium) from Livewire Puzzles
More informationREVIEW ON LATIN SQUARE
Available Online at www.ijcsmc.com International Journal of Computer Science and Mobile Computing A Monthly Journal of Computer Science and Information Technology IJCSMC, Vol. 3, Issue. 7, July 2014, pg.338
More informationPermutations and codes:
Hamming distance Permutations and codes: Polynomials, bases, and covering radius Peter J. Cameron Queen Mary, University of London p.j.cameron@qmw.ac.uk International Conference on Graph Theory Bled, 22
More informationIntroducing: second-order permutation and corresponding second-order permutation factorial
Introducing: second-order permutation and corresponding second-order permutation factorial Bassey Godwin Bassey JANUARY 2019 1 Abstract In this study we answer questions that have to do with finding out
More informationIntegrated Strategy for Generating Permutation
Int J Contemp Math Sciences, Vol 6, 011, no 4, 1167-1174 Integrated Strategy for Generating Permutation Sharmila Karim 1, Zurni Omar and Haslinda Ibrahim Quantitative Sciences Building College of Arts
More informationA Course in Model Theory I:
A Course in Model Theory I: Introduction 1 Rami Grossberg DEPARTMENT OFMATHEMATICAL SCIENCES, CARNEGIE MELLON UNI- VERSITY, PITTSBURGH, PA15213 1 This preliminary draft is dated from August 15, 2017. The
More informationMobile Broadband Multimedia Networks
Mobile Broadband Multimedia Networks Techniques, Models and Tools for 4G Edited by Luis M. Correia v c» -''Vi JP^^fte«jfc-iaSfllto ELSEVIER AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN
More informationA Course in Model Theory
A Course in Model Theory Author address: Rami Grossberg 1 DEPARTMENT OF MATHEMATICAL SCIENCES, CARNEGIE MELLON UNI- VERSITY, PITTSBURGH, PA 15213 E-mail address: rami@cmu.edu 1 This preliminary draft is
More informationOn Kaleidoscope Designs
On Kaleidoscope Designs Francesca Merola Roma Tre University Joint work with Marco Buratti notation (v, k, λ)-design: V = v set of points, B set of blocks, B ( V k ), B = b, such that any two points belong
More informationLower Bounds for the Number of Bends in Three-Dimensional Orthogonal Graph Drawings
ÂÓÙÖÒÐ Ó ÖÔ ÐÓÖØÑ Ò ÔÔÐØÓÒ ØØÔ»»ÛÛÛº ºÖÓÛÒºÙ»ÔÙÐØÓÒ»» vol.?, no.?, pp. 1 44 (????) Lower Bounds for the Number of Bends in Three-Dimensional Orthogonal Graph Drawings David R. Wood School of Computer Science
More informationWeek 1. 1 What Is Combinatorics?
1 What Is Combinatorics? Week 1 The question that what is combinatorics is similar to the question that what is mathematics. If we say that mathematics is about the study of numbers and figures, then combinatorics
More informationA Course in Model Theory
A Course in Model Theory Author address: Rami Grossberg 1 DEPARTMENT OF MATHEMATICAL SCIENCES, CARNEGIE MELLON UNI- VERSITY, PITTSBURGH, PA 15213 E-mail address: rami@cmu.edu 1 This preliminary draft is
More information17. Symmetries. Thus, the example above corresponds to the matrix: We shall now look at how permutations relate to trees.
7 Symmetries 7 Permutations A permutation of a set is a reordering of its elements Another way to look at it is as a function Φ that takes as its argument a set of natural numbers of the form {, 2,, n}
More informationSolutions to Exercises Chapter 6: Latin squares and SDRs
Solutions to Exercises Chapter 6: Latin squares and SDRs 1 Show that the number of n n Latin squares is 1, 2, 12, 576 for n = 1, 2, 3, 4 respectively. (b) Prove that, up to permutations of the rows, columns,
More informationBiembeddings of Latin squares and Hamiltonian decompositions
Biembeddings of Latin squares and Hamiltonian decompositions M. J. Grannell, T. S. Griggs Department of Pure Mathematics The Open University Walton Hall Milton Keynes MK7 6AA UNITED KINGDOM M. Knor Department
More informationPD-SETS FOR CODES RELATED TO FLAG-TRANSITIVE SYMMETRIC DESIGNS. Communicated by Behruz Tayfeh Rezaie. 1. Introduction
Transactions on Combinatorics ISSN (print): 2251-8657, ISSN (on-line): 2251-8665 Vol. 7 No. 1 (2018), pp. 37-50. c 2018 University of Isfahan www.combinatorics.ir www.ui.ac.ir PD-SETS FOR CODES RELATED
More informationThe Mathematics of Geometrical and Physical Optics
Orestes N. Stavroudis The Mathematics of Geometrical and Physical Optics The fc-function and its Ramifications WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA I Preliminaries 1 1 Fermat's Principle and the
More informationAn Introduction to Discrete Mathematics in the Classroom: Latin Squares. Students Guide
LatinSquares Benson/King/Mudrock An Introduction to Discrete Mathematics in the Classroom: Latin Squares Students Guide Carol T. Benson, Illinois State University Kyle P. King, University of Illinois Jeffrey
More informationReflections on the N + k Queens Problem
Integre Technical Publishing Co., Inc. College Mathematics Journal 40:3 March 12, 2009 2:02 p.m. chatham.tex page 204 Reflections on the N + k Queens Problem R. Douglas Chatham R. Douglas Chatham (d.chatham@moreheadstate.edu)
More informationElectromagnetic Waveguides and Transmission Lines
Electromagnetic Waveguides and Transmission Lines FRANK OLYSLAGER Department of Information Technology University of Gent CLARENDON PRESS OXFORD 1999 CONTENTS List of symbols xv 1 Introduction 1 1.1 Historical
More informationINFLUENCE OF ENTRIES IN CRITICAL SETS OF ROOM SQUARES
INFLUENCE OF ENTRIES IN CRITICAL SETS OF ROOM SQUARES Ghulam Chaudhry and Jennifer Seberry School of IT and Computer Science, The University of Wollongong, Wollongong, NSW 2522, AUSTRALIA We establish
More informationName Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines
Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines Two lines are if they are coplanar and do not intersect. Skew lines. Two
More informationPeter J. Cameron, London, 1991
Preface It is common now in academic circles to lament the decline in the teaching of geometry in our schools and universities, and the resulting loss of geometric intuition among our students. On the
More informationSome t-homogeneous sets of permutations
Some t-homogeneous sets of permutations Jürgen Bierbrauer Department of Mathematical Sciences Michigan Technological University Houghton, MI 49931 (USA) Stephen Black IBM Heidelberg (Germany) Yves Edel
More informationOpen Research Online The Open University s repository of research publications and other research outputs
Open Research Online The Open University s repository of research publications and other research outputs Icosahedron designs Journal Item How to cite: Forbes, A. D. and Griggs, T. S. (2012). Icosahedron
More informationCoherent Configurations
Coherent Configurations Lecture 10: Miscellanea: Some research tasks in AGT Mikhail Klin (Ben-Gurion University) September 1 5, 2014 M. Klin (BGU) Miscellanea 1 / 67 Preamble We will discuss a number of
More information8.3 Prove It! A Practice Understanding Task
15 8.3 Prove It! A Practice Understanding Task In this task you need to use all the things you know about quadrilaterals, distance, and slope to prove that the shapes are parallelograms, rectangles, rhombi,
More informationDividing Ranks into Regiments using Latin Squares
Dividing Ranks into Regiments using Latin Squares James Hammer Department of Mathematics and Statistics Auburn University August 2, 2013 1 / 22 1 Introduction Fun Problem Definition Theory Rewording the
More informationWireless Communications Over Rapidly Time-Varying Channels
Wireless Communications Over Rapidly Time-Varying Channels Edited by Franz Hlawatsch Gerald Matz ELSEVIER AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY
More informationarxiv: v2 [math.ho] 23 Aug 2018
Mathematics of a Sudo-Kurve arxiv:1808.06713v2 [math.ho] 23 Aug 2018 Tanya Khovanova Abstract Wayne Zhao We investigate a type of a Sudoku variant called Sudo-Kurve, which allows bent rows and columns,
More informationCrossings and patterns in signed permutations
Crossings and patterns in signed permutations Sylvie Corteel, Matthieu Josuat-Vergès, Jang-Soo Kim Université Paris-sud 11, Université Paris 7 Permutation Patterns 1/28 Introduction A crossing of a permutation
More informationMultivariate Permutation Tests: With Applications in Biostatistics
Multivariate Permutation Tests: With Applications in Biostatistics Fortunato Pesarin University ofpadova, Italy JOHN WILEY & SONS, LTD Chichester New York Weinheim Brisbane Singapore Toronto Contents Preface
More informationLatin Squares for Elementary and Middle Grades
Latin Squares for Elementary and Middle Grades Yul Inn Fun Math Club email: Yul.Inn@FunMathClub.com web: www.funmathclub.com Abstract: A Latin square is a simple combinatorial object that arises in many
More informationSome Cryptanalysis of the Block Cipher BCMPQ
Some Cryptanalysis of the Block Cipher BCMPQ V. Dimitrova, M. Kostadinoski, Z. Trajcheska, M. Petkovska and D. Buhov Faculty of Computer Science and Engineering Ss. Cyril and Methodius University, Skopje,
More informationSynchronization in Digital Communications
Synchronization in Digital Communications Volume 1 Phase-, Frequency-Locked Loops, and Amplitude Control Heinrich Meyr Aachen University of Technology (RWTH) Gerd Ascheid CADIS GmbH, Aachen WILEY A Wiley-lnterscience
More informationCONTENTS. Cambridge University Press Vibration of Mechanical Systems Alok Sinha Table of Contents More information
CONTENTS Preface page xiii 1 Equivalent Single-Degree-of-Freedom System and Free Vibration... 1 1.1 Degrees of Freedom 3 1.2 Elements of a Vibratory System 5 1.2.1 Mass and/or Mass-Moment of Inertia 5
More informationMEI Conference Short Open-Ended Investigations for KS3
MEI Conference 2012 Short Open-Ended Investigations for KS3 Kevin Lord Kevin.lord@mei.org.uk 10 Ideas for Short Investigations These are some of the investigations that I have used many times with a variety
More information1 Algebraic substructures
Permutation codes Peter J. Cameron School of Mathematical Sciences Queen Mary, University of London Mile End Road London E1 4NS UK p.j.cameron@qmul.ac.uk Abstract There are many analogies between subsets
More informationMULTIPATH fading could severely degrade the performance
1986 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 53, NO. 12, DECEMBER 2005 Rate-One Space Time Block Codes With Full Diversity Liang Xian and Huaping Liu, Member, IEEE Abstract Orthogonal space time block
More informationCONTENTS GRAPH THEORY
CONTENTS i GRAPH THEORY GRAPH THEORY By Udit Agarwal M.Sc. (Maths), M.C.A. Sr. Lecturer, Rakshpal Bahadur Management Institute, Bareilly Umeshpal Singh (MCA) Director, Rotary Institute of Management and
More informationYou ve seen them played in coffee shops, on planes, and
Every Sudoku variation you can think of comes with its own set of interesting open questions There is math to be had here. So get working! Taking Sudoku Seriously Laura Taalman James Madison University
More informationName: Date: Chapter 2 Quiz Geometry. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Date: Chapter 2 Quiz Geometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the value of x? Identify the missing justifications.,, and.
More informationTaking Sudoku Seriously
Taking Sudoku Seriously Laura Taalman, James Madison University You ve seen them played in coffee shops, on planes, and maybe even in the back of the room during class. These days it seems that everyone
More informationConsider the following cyclic 4 ~
On Embeddi~g a Mateless Latin Square In a Complete Set of Orthogonal F-Squares John P. Mandeli Virginia Commonwealth Un!veraity Walter T. Federer Cornell University This paper. gives an example of a latin
More informationFind the coordinates of the midpoint of a segment having the given endpoints.
G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to
More informationCO-ORDINATE GEOMETRY CHAPTER 3. Points to Remember :
CHAPTER Points to Remember : CO-ORDINATE GEOMETRY 1. Coordinate axes : Two mutually perpendicular lines X OX and YOY known as x-axis and y-axis respectively, constitutes to form a co-ordinate axes system.
More informationContents Preface Micro-Doppler Signatures Review, Challenges, and Perspectives Phenomenology of Radar Micro-Doppler Signatures
Contents Preface xi 1 Micro-Doppler Signatures Review, Challenges, and Perspectives 1 1.1 Introduction 1 1.2 Review of Micro-Doppler Effect in Radar 2 1.2.1 Micro-Doppler Signatures of Rigid Body Motion
More informationOrthomorphisms of Boolean Groups. Nichole Louise Schimanski. A dissertation submitted in partial fulfillment of the requirements for the degree of
Orthomorphisms of Boolean Groups by Nichole Louise Schimanski A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematical Sciences Dissertation
More informationOnline Computation and Competitive Analysis
Online Computation and Competitive Analysis Allan Borodin University of Toronto Ran El-Yaniv Technion - Israel Institute of Technology I CAMBRIDGE UNIVERSITY PRESS Contents Preface page xiii 1 Introduction
More informationAn Optimal Algorithm for a Strategy Game
International Conference on Materials Engineering and Information Technology Applications (MEITA 2015) An Optimal Algorithm for a Strategy Game Daxin Zhu 1, a and Xiaodong Wang 2,b* 1 Quanzhou Normal University,
More informationORTHOGONAL space time block codes (OSTBC) from
1104 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 55, NO. 3, MARCH 2009 On Optimal Quasi-Orthogonal Space Time Block Codes With Minimum Decoding Complexity Haiquan Wang, Member, IEEE, Dong Wang, Member,
More informationSudoku: Is it Mathematics?
Sudoku: Is it Mathematics? Peter J. Cameron Forder lectures April 2008 There s no mathematics involved. Use logic and reasoning to solve the puzzle. Instructions in The Independent There s no mathematics
More informationDigital Signal Processing
Digital Signal Processing Fourth Edition John G. Proakis Department of Electrical and Computer Engineering Northeastern University Boston, Massachusetts Dimitris G. Manolakis MIT Lincoln Laboratory Lexington,
More informationCONSTRUCTIONS OF ORTHOGONAL F(2k, q) SQUARES
CONSTRUCTIONS OF ORTHOGONAL F(k, q) SQUARES By Walter T. Federer Department of Biological Statistics and Computational Biology and Department of Statistical Sciences, Cornell University ABSTRACT Anderson
More information4. Magic Squares, Latin Squares and Triple Systems Robin Wilson
4. Magic Squares, Latin Squares and Triple Systems Robin Wilson Square patterns The Lo-shu diagram The Lo-shu had magical significance for example, relating to nine halls of a mythical palace where rites
More informationA year ago I investigated a mathematical problem relating to Latin squares. Most people, whether knowing it or not, have actually seen a Latin square
1 How I Got Started: A year ago I investigated a mathematical problem relating to Latin squares. Most people, whether knowing it or not, have actually seen a Latin square at some point in their lives and
More informationStep 2: Extend the compass from the chosen endpoint so that the width of the compass is more than half the distance between the two points.
Student Name: Teacher: Date: District: Miami-Dade County Public Schools Test: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the given
More informationCONTENTS PREFACE. Part One THE DESIGN PROCESS: PROPERTIES, PARADIGMS AND THE EVOLUTIONARY STRUCTURE
Copyrighted Material Dan Braha and Oded Maimon, A Mathematical Theory of Design: Foundations, Algorithms, and Applications, Springer, 1998, 708 p., Hardcover, ISBN: 0-7923-5079-0. PREFACE Part One THE
More informationGeometry Vocabulary Book
Geometry Vocabulary Book Units 2-4 Page 1 Unit 2 General Geometry Point Characteristics: Line Characteristics: Plane Characteristics: RELATED POSTULATES: Through any two points there exists exactly one
More informationComputational Principles of Mobile Robotics
Computational Principles of Mobile Robotics Mobile robotics is a multidisciplinary field involving both computer science and engineering. Addressing the design of automated systems, it lies at the intersection
More informationAlgorithmic Number Theory and Cryptography (CS 303)
Algorithmic Number Theory and Cryptography (CS 303) Modular Arithmetic Jeremy R. Johnson 1 Introduction Objective: To become familiar with modular arithmetic and some key algorithmic constructions that
More informationMUMS seminar 24 October 2008
MUMS seminar 24 October 2008 Tiles have been used in art and architecture since the dawn of civilisation. Toddlers grapple with tiling problems when they pack away their wooden blocks and home renovators
More informationTHE ASSOCIATION OF MATHEMATICS TEACHERS OF NEW JERSEY 2018 ANNUAL WINTER CONFERENCE FOSTERING GROWTH MINDSETS IN EVERY MATH CLASSROOM
THE ASSOCIATION OF MATHEMATICS TEACHERS OF NEW JERSEY 2018 ANNUAL WINTER CONFERENCE FOSTERING GROWTH MINDSETS IN EVERY MATH CLASSROOM CREATING PRODUCTIVE LEARNING ENVIRONMENTS WEDNESDAY, FEBRUARY 7, 2018
More informationSystem analysis and signal processing
System analysis and signal processing with emphasis on the use of MATLAB PHILIP DENBIGH University of Sussex ADDISON-WESLEY Harlow, England Reading, Massachusetts Menlow Park, California New York Don Mills,
More information8.2 Slippery Slopes. A Solidify Understanding Task
7 8.2 Slippery Slopes A Solidify Understanding Task CC BY https://flic.kr/p/kfus4x While working on Is It Right? in the previous module you looked at several examples that lead to the conclusion that the
More informationGrade 4 Mathematics Indiana Academic Standards Crosswalk
Grade 4 Mathematics Indiana Academic Standards Crosswalk 2014 2015 The Process Standards demonstrate the ways in which students should develop conceptual understanding of mathematical content and the ways
More informationTHE SIGN OF A PERMUTATION
THE SIGN OF A PERMUTATION KEITH CONRAD 1. Introduction Throughout this discussion, n 2. Any cycle in S n is a product of transpositions: the identity (1) is (12)(12), and a k-cycle with k 2 can be written
More informationNEW Published in June 2018 CATALOGUE 2019
NEW Published in June 2018 CATALOGUE 2019 PASS PUBLICATIONS PRIVATE ACADEMIC AND SCIENTIFIC STUDIES LIMITED passpublications.uk@gmail.com +44(0)20 8857 4752 P A S S PUBLICATIONS PASS is an acronym for
More informationPermutation groups, derangements and prime order elements
Permutation groups, derangements and prime order elements Tim Burness University of Southampton Isaac Newton Institute, Cambridge April 21, 2009 Overview 1. Introduction 2. Counting derangements: Jordan
More informationAGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School
AGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School Copyright 2008 Pearson Education, Inc. or its affiliate(s). All rights reserved AGS Math Algebra 2 Grade
More informationFILTER BANK TRANSCEIVERS FOR OFDM AND DMT SYSTEMS
FILTER BANK TRANSCEIVERS FOR OFDM AND DMT SYSTEMS YUAN-PEI LIN National Chiao Tung University, Taiwan SEE-MAY PHOONG National Taiwan University P. P. VAIDYANATHAN California Institute of Technology CAMBRIDGE
More informationOn the isomorphism problem of Coxeter groups and related topics
On the isomorphism problem of Coxeter groups and related topics Koji Nuida 1 Graduate School of Mathematical Sciences, University of Tokyo E-mail: nuida@ms.u-tokyo.ac.jp At the conference the author gives
More informationTable of Contents. Frequently Used Abbreviation... xvii
GPS Satellite Surveying, 2 nd Edition Alfred Leick Department of Surveying Engineering, University of Maine John Wiley & Sons, Inc. 1995 (Navtech order #1028) Table of Contents Preface... xiii Frequently
More informationTHINGS TO DO WITH A GEOBOARD
THINGS TO DO WITH A GEOBOARD The following list of suggestions is indicative of exercises and examples that can be worked on the geoboard. Simpler, as well as, more difficult suggestions can easily be
More informationContents Systems of Linear Equations and Determinants
Contents 6. Systems of Linear Equations and Determinants 2 Example 6.9................................. 2 Example 6.10................................ 3 6.5 Determinants................................
More informationBibliography. S. Gill Williamson
Bibliography S. Gill Williamson 1. S. G. Williamson, A Combinatorial Property of Finite Sequences with Applications to Tensor Algebra, J. Combinatorial Theory, 1 (1966), pp. 401-410. 2. S. G. Williamson,
More informationAdvances in Direction-of-Arrival Estimation
Advances in Direction-of-Arrival Estimation Sathish Chandran Editor ARTECH HOUSE BOSTON LONDON artechhouse.com Contents Preface xvii Acknowledgments xix Overview CHAPTER 1 Antenna Arrays for Direction-of-Arrival
More informationON OPTIMAL (NON-TROJAN) SEMI-LATIN SQUARES WITH SIDE n AND BLOCK SIZE n: CONSTRUCTION PROCEDURE AND ADMISSIBLE PERMUTATIONS
Available at: http://wwwictpit/~pub off IC/2006/114 United Nations Educational, Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL
More informationArithmetic Sequences Read 8.2 Examples 1-4
CC Algebra II HW #8 Name Period Row Date Arithmetic Sequences Read 8.2 Examples -4 Section 8.2 In Exercises 3 0, tell whether the sequence is arithmetic. Explain your reasoning. (See Example.) 4. 2, 6,
More informationPerfect Difference Families and Related Variable-Weight Optical Orthogonal Codess
Perfect Difference Families and Related Variable-Weight Optical Orthogonal Codess D. Wu, M. Cheng, Z. Chen Department of Mathematics Guangxi Normal University Guilin 541004, China Abstract Perfect (v,
More informationPermutation decoding: an update
Permutation decoding: an update J. D. Key Department of Mathematical Sciences Clemson University Clemson SC 29634 U.S.A. March 29, 2003 Abstract We give a brief survey of permutation decoding and some
More informationPrecoding and Signal Shaping for Digital Transmission
Precoding and Signal Shaping for Digital Transmission Robert F. H. Fischer The Institute of Electrical and Electronics Engineers, Inc., New York WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
More informationPRIMES STEP Plays Games
PRIMES STEP Plays Games arxiv:1707.07201v1 [math.co] 22 Jul 2017 Pratik Alladi Neel Bhalla Tanya Khovanova Nathan Sheffield Eddie Song William Sun Andrew The Alan Wang Naor Wiesel Kevin Zhang Kevin Zhao
More informationON 4-DIMENSIONAL CUBE AND SUDOKU
ON 4-DIMENSIONAL CUBE AND SUDOKU Marián TRENKLER Abstract. The number puzzle SUDOKU (Number Place in the U.S.) has recently gained great popularity. We point out a relationship between SUDOKU and 4- dimensional
More informationEdge-disjoint tree representation of three tree degree sequences
Edge-disjoint tree representation of three tree degree sequences Ian Min Gyu Seong Carleton College seongi@carleton.edu October 2, 208 Ian Min Gyu Seong (Carleton College) Trees October 2, 208 / 65 Trees
More informationEnumeration of Pin-Permutations
Enumeration of Pin-Permutations Frédérique Bassino, athilde Bouvel, Dominique Rossin To cite this version: Frédérique Bassino, athilde Bouvel, Dominique Rossin. Enumeration of Pin-Permutations. 2008.
More informationHANDS-ON TRANSFORMATIONS: RIGID MOTIONS AND CONGRUENCE (Poll Code 39934)
HANDS-ON TRANSFORMATIONS: RIGID MOTIONS AND CONGRUENCE (Poll Code 39934) Presented by Shelley Kriegler President, Center for Mathematics and Teaching shelley@mathandteaching.org Fall 2014 8.F.1 8.G.1a
More informationThe pairing strategies of the 9-in-a-row game
ISSN 1855-3966 (printed edn.), ISSN 1855-3974 (electronic edn.) ARS MATHEMATICA CONTEMPORANEA 16 (2019) 97 109 https://doi.org/10.26493/1855-3974.1350.990 (Also available at http://amc-journal.eu) The
More informationQäf) Newnes f-s^j^s. Digital Signal Processing. A Practical Guide for Engineers and Scientists. by Steven W. Smith
Digital Signal Processing A Practical Guide for Engineers and Scientists by Steven W. Smith Qäf) Newnes f-s^j^s / *" ^"P"'" of Elsevier Amsterdam Boston Heidelberg London New York Oxford Paris San Diego
More informationAalborg Universitet. Chapter on The history of latin squares Andersen, Lars Døvling. Publication date: 2007
Aalborg Universitet Chapter on The history of latin squares Andersen, Lars Døvling Publication date: 2007 Document Version Publisher's PDF, also known as Version of record Link to publication from Aalborg
More informationCLASSIFICATION OF LATIN SQUARES. Dr Nada Lakić
Journal of Agricultural Sciences Vol. 47, No 1, 2002 Pages 105-112 UDC: 311 Review articles CLASSIFICATION OF LATIN SQUARES Dr Nada Lakić Abstract: Efficacy and profitability of results and eventually
More informationResearch Article The Structure of Reduced Sudoku Grids and the Sudoku Symmetry Group
International Combinatorics Volume 2012, Article ID 760310, 6 pages doi:10.1155/2012/760310 Research Article The Structure of Reduced Sudoku Grids and the Sudoku Symmetry Group Siân K. Jones, Stephanie
More informationApplications of Advanced Mathematics (C4) Paper B: Comprehension INSERT WEDNESDAY 21 MAY 2008 Time:Upto1hour
ADVANCED GCE 4754/01B MATHEMATICS (MEI) Applications of Advanced Mathematics (C4) Paper B: Comprehension INSERT WEDNESDAY 21 MAY 2008 Afternoon Time:Upto1hour INSTRUCTIONS TO CANDIDATES This insert contains
More informationTHE REMOTENESS OF THE PERMUTATION CODE OF THE GROUP U 6n. Communicated by S. Alikhani
Algebraic Structures and Their Applications Vol 3 No 2 ( 2016 ) pp 71-79 THE REMOTENESS OF THE PERMUTATION CODE OF THE GROUP U 6n MASOOMEH YAZDANI-MOGHADDAM AND REZA KAHKESHANI Communicated by S Alikhani
More informationMULTIPLES, FACTORS AND POWERS
The Improving Mathematics Education in Schools (TIMES) Project MULTIPLES, FACTORS AND POWERS NUMBER AND ALGEBRA Module 19 A guide for teachers - Years 7 8 June 2011 7YEARS 8 Multiples, Factors and Powers
More informationDigital Signal Processing
Digital Signal Processing System Analysis and Design Paulo S. R. Diniz Eduardo A. B. da Silva and Sergio L. Netto Federal University of Rio de Janeiro CAMBRIDGE UNIVERSITY PRESS Preface page xv Introduction
More information