C o n n e c t i n g G r e a t M i n d s

P r e f e r r e d P u b l i s h e r f o r L e a d i n g T h i n k e r s

❖ Solution Manual Available

Monographs in Number Theory – Vol. 7

THE THEORY OF MULTIPLE ZETA VALUES WITH APPLICATIONS IN COMBINATORICSby Minking Eie (National Chung Cheng University, Taiwan)

This is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics, and numerous interesting identities are produced that are ready to be used. This will provide a powerful tool to deal with problems in multiple zeta values, both in evaluations and shuffle relations. The volume will benefit graduate students doing research in number theory.

Contents: Basic Theory of Multiple Zeta Values: The Time Before Multiple Zeta Values; Introduction to the Theory of Multiple Zeta Values; The Sum Formula; Shuffle Relations among Multiple Zeta Values: Some Shuffle Relations; Euler Decomposition Theorem; Multiple Zeta Values of Height Two; Applications of Shuffle Relations in Combinatorics: Generalizations of Pascal Identity; Combinatorial Identities of Convolution Type; Vector Version of Some Combinatorial Identities; Appendices: Singular Modular Forms on the Exceptional Domain; Shuffle Product Formulas of Multiple Zeta Values; The Sum Formula, the Restricted Sum Formula, their Generalizations and Applications.

280pp Aug 2013978-981-4472-63-0 US$68    £45

Essential Titles in Combinatorics & Graph Theory

✺ Bestselling Textbook

A WALK THROUGH COMBINATORICSAn Introduction to Enumeration and Graph Theoryby Miklós Bóna (University of Florida, USA)

“The chapters on block designs and counting unlabeled structures have been added to the third edition, and there are also one hundred new problems in the other eighteen chapters. When I next teach a combinatorics course, this will be the text I use.”

Mathematical Reviews

Review of the Second Edition:

“Bóna’s book is an excellent choice for anyone who wants an introduction to this beautiful branch of mathematics … Plentiful examples illustrate each of the topics included in the book. Bóna does a supreme job of walking us through combinatorics.”

CHOICE

This is a textbook for an introductory combinatorics course lasting one or two semesters. Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.

Contents: Basic Methods Seven is More Than Six. The Pigeon-Hole Principle; One Step at a Time. The Method of Mathematical Induction; Enumerative Combinatorics There are a Lot of Them. Elementary Counting Problems; No Matter How You Slice It. The Binomial Theorem and Related Identities; Divide and Conquer. Partitions; Not So Vicious Cycles. Cycles in Permutations; You Shall Not Overcount. The Sieve; A Function is Worth Many Numbers. Generating Functions; Graph Theory Dots and Lines. The Origins of Graph Theory; Staying Connected. Trees; Finding a Good Match. Coloring and Matching; Do Not Cross. Planar Graphs; Horizons Does It clique? Ramsey Theory; So Hard to Avoid. Subsequence Conditions on Permutations; Who Knows What It Looks Like, But It Exists. The Probabilistic Method; At Least Some Order. Partial Orders and Lattices; As Evenly as Possible. Block Designs and Error Correcting Codes; Are They Really Different? Counting Unlabeled Structures; The Sooner the Better. Combinatorial Algorithms; Does Many Mean More Than One? Computational Complexity.

Paperback Available in Aug 2013

568pp May 2011978-981-4335-23-2 US$110 £72

978-981-4460-00-2(pbk) US$58 £38

✴Third Edition

2 www.worldscientific.com

Essential Titles in Combinatorics & Graph Theory

Peking University Series in Mathematics – Vol. 5

DIFFERENCE SETS AND THEIR APPLICATIONSby Weisheng Qiu (Peking University, China)

Contents: Stream Cipher and Difference Sets; Symmetric Designs and Difference Sets; Algebraic Approach for Studying Difference Sets; Multipliers and Multiplier Conjecture; Difference Sets with Singer Parameters; Paley-Hadamard Difference Sets; Skew Difference Sets; Planar Difference Sets; Prime Power Conjecture; Lander Conjecture; Bent Functions and Hadamard Difference Sets; The other Difference Sets with gcd(v,n)>1. Schmidt’s Exponent Bound; Perfect Nonlinear Maps for Preventing Differential Cryptanalysis; Relative Difference Sets.

300pp Nov 2013978-981-4280-76-1 US$88    £61

COUNTING (Second Edition)by Khee Meng Koh (National University of Singapore) & Eng Guan Tay (Nanyang Technological University, Singapore)

The new chapters include the Principle of Inclusion and Exclusion, the Pigeonhole Principle, Recurrence Relations, the Stirling Numbers and the Catalan Numbers. A number of new problems have also been added to this edition.

Contents: The Addition Principle; The Multiplication Principle; Subsets and Arrangements; Applications; The Bijection Principle; Distribution of Balls into Boxes; More Applications of (BP); Distribution of Distinct Objects into Distinct Boxes; Other Variations of the Distribution Problem; The Binomial Expansion; Some Useful Identities; Pascal’s Triangle; The Principle of Inclusion and Exclusion; General Statement of the Principle of Inclusion and Exclusion; The Pigeonhole Principle; Recurrence Relations; The Stirling Numbers of the First Kind; The Stirling Numbers of the Second Kind; The Catalan Numbers; Miscellaneous Problems.

224pp Mar 2013978-981-4401-90-6 US$58    £38978-981-4401-91-3(pbk) US$28    £18

This book is the essential companion to above book.

224pp May 2013978-981-4401-94-4(pbk) US$42    £28

ICP Selected Papers – Vol. 3

THE SELECTED WORKS OF GEORGE E ANDREWS(With Commentary)by George E Andrews (Pennsylvania State University, USA) & edited by Andrew V Sills (Georgia Southern University, USA)

George E Andrews is the Evan Pugh Professor of Mathematics at Pennsylvania State University. He is also President of the American Mathematical Society (AMS) for the period of 2009–2011. He is a world pioneer in partitions and q-series and his contributions include more than 250 scientific papers and several books on number theory and the theory of partitions. In 1976 he discovered Ramanujan’s Lost Notebook, a finding which changed the shape of modern q-series research.

Contents: The Geometry of Numbers; q-Series; Partition Identities; Plane Partitions; Combinatorics, Fibonacci Numbers, and Computers; Number Theory; Surveys; Education, History, etc.

1060pp Dec 2012978-1-84816-666-0 US$298    £185

POLYGROUP THEORY AND RELATED SYSTEMSby Bijan Davvaz (Yazd University, Iran)

This monograph is devoted to the study of Polygroup Theory. It begins with some basic results concerning group theory and algebraic hyperstructures, which represent the most general algebraic context, in which reality can be modeled. Most results on polygroups are collected in this book. Moreover, this monograph is the first book on this theory. The volume is highly recommended to theoreticians in pure and applied mathematics.

208pp Sep 2012978-981-4425-30-8 US$44    £29

Series on Knots and Everything – Vol. 51

VIRTUAL KNOTSThe State of the Artby Vassily Olegovich Manturov (Peoples’ Friendship University of Russia, Russia) & Denis Petrovich Ilyutko (Moscow State University, Russia & Yaroslavl State University, Russia)

“We hope that the reader of this review is motivated to delve into the adventure presented by this remarkable book.”

Journal of Knot Theory and Its Ramifications

“The book is highly recommended to under gradua te s , g radua te s , professionals and amateur mathe-maticians, because it goes from the basics to the frontiers of research.”

The European Mathematical Society

552pp Sep 2012978-981-4401-12-8 US$168    £111

Algebra and Discrete Mathematics – Vol. 3

LECTURES ON DISCRETE MATHEMATICS FOR COMPUTER SCIENCEby Bakhadyr Khoussainov (University of Auckland, New Zealand) & Nodira Khoussainova (University of Washington, USA)

Contents: Definitions, Theorems, and Proofs; Proof Methods; Integers and Divisibility; Euclidean Algorithm and Congruence Relations; Secret Message Passing; Basics of Directed Graphs; The Path Problem and Undirected Graphs; Circuit Problems in Graphs; Rooted Trees; Sets and Operations on Sets; Relations on Sets; Equivalence Relations and Partial Orders; Databases and Relational Structures; Relational Calculus; Program Correctness Through Loop Invariants; Induction and Recursion; Spanning Trees; Shortest Paths in Directed Weighted Graphs; Games Played on Finite Graphs; Functions; Types of Functions; Syntax of Propositional Logic; Semantics of Propositional Logic; Normal Forms and the SAT Problem; Deterministic Finite Automata; Designing Finite Automata; Nondeterministic Finite Automata; The Subset Construction; Regular Expressions and Finite Automata; Algorithms for Finite Automata; Counting Principles; Permutations and Combinations; Basics of Probability.

364pp Mar 2012978-981-4340-50-2 US$69    £46

✺ Textbook

✺ Textbook❖ Solution Manual

3www.icpress.co.uk

WORLD SCIENTIFIC ~ IMPERIAL COLLEGE PRESS

BESTSELLING TITLES

OPERATOR CALCULUS ON GRAPHSTheory and Applications in Computer Scienceby René Schott (IECN and LORIA, Université Henri Poincaré, Nancy, France) & G Stacey Staples (Southern Illinois University Edwardsville, USA)

This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science.

Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with packages for performing symbolic computations.

428pp Feb 2012978-1-84816-876-3 US$134    £88

FIGURATE NUMBERSby Elena Deza (Moscow State Pedagogical University, Russia) & Michel Marie Deza (Ecole Normale Superieure, Paris, France)

Figurate numbers have a rich history with many applications. The main purpose of this book is to provide a thorough and complete presentation of the theory of figurate numbers, giving much of their properties, facts and theorems with full proofs. This book is the first of this topic written in unified systematic way. It also contains many exercises with solutions.

Contents: Plane Figurate Numbers; Space Figurate Numbers; Multidimensional Figurate Numbers; Areas of Number Theory including Figurate Numbers; Fermat’s Polygonal Number Theorem; Zoo of Figurate-related Numbers.

476pp Jan 2012978-981-4355-48-3 US$155    £102

GEOMETRY, PERSPECTIVE DRAWING, AND MECHANISMSby Donald Row (University of Tasmania, Australia) & Talmage James Reid (University of Mississippi, USA)

“It does provide ample opportunity for assignments, guiding teachers to design class projects involving perspective, binocular vision, or mechanisms that can engage students who otherwise may find geometry quite abstruse. This novel approach deserves serious consideration.”

MAA Reviews

“Students and instructors in mathematics can find an original approach to projective geometry and several applications. Students and specialists in computer science will become acquainted with an axiomatic way for the description of natural objects. The book is intended for students in mathematics, computer science and for lecturers and scientists who need a working knowledge of applied geometry.”

Zentralblatt MATH

340pp Nov 2011978-981-4343-82-4 US$82    £53

COMBINATORIAL PROBLEMS IN MATHEMATICAL COMPETITIONSby Yao Zhang (Hunan Normal University, China)

This book focuses on combinatorial problems in mathematical competitions. It provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces important solutions to combinatorial problems and some typical problems with often-used solutions. Some enlightening and novel examples and exercises are well chosen in this book.

Contents: Fundamental Knowledge: Principles and Formulas of Counting; Pigeonhole Principle and Mean Value Principle; The Generating Functions; Recurrence Sequence of Numbers; Basic Method: Classification and Method of Fractional Steps; Correspondent Method; Counting in Two Ways; Recurrence Method; Coloring Method and Evaluation Method; Reduction to Absurdity and the Extreme Principle; Local Adjustment Method; Constructive Method; Typical Problems: Combinatorial Counting Problems; Existence Problems and the Proof of Inequalities in Combinatorial Problems; Combinatorial Extremum Problems.

304pp Mar 2011978-981-283-949-7(pbk) US$34    £22

GRAPH THEORYby Bin Xiong (East China Normal University, China), Zhongyi Zheng (High School Attached to Fudan University, China), translated by Ruifang Liu, Mingqing Zhai & Yuanqing Lin (East China Normal University, China)

In 1736, the mathematician Euler invented graph theory while solving the Konigsberg seven-bridge problem. Over 200 years later, graph theory remains the skeleton content of discrete mathematics, which serves as a theoretical basis for computer science and network information science. This book introduces some basic knowledge and the primary methods in graph theory by many interesting problems and games.

Contents: Definition of Graph; Degree of a Vertex; Turán’s Theorem; Tree; Euler’s Problem; Hamilton’s Problem; Planar Graph; Ramsey’s Problem; Tournament.

156pp Mar 2010978-981-4271-12-7(pbk) US$34    £22

DISCRETE MATHEMATICS, ALGORITHMSAND APPLICATIONS (DMAA)

Print / Online ISSN: 1793-8309 / 1793-8317http://www.worldscinet.com/dmaa

The aim of this journal is to advance and promote the theory and applications of discrete mathematics, which is a research area in mathematics with applications in computer science, industrial engineering, bio-informatics, chemistry and communication networks. The journal encourages contributions from the two important parts of discrete mathematics, graph theory and combinatorics. The former includes structural graph theory, extremal graph theory, algebraic graph theory, random graphs and internet graphs. The latter consists of combinatorial design, combinatorial enumeration, coding theory, combinatorial probabilistic method, etc.

Co-Editors-in-ChiefDing-Zhu Du, University of Texas at Dallas, USAJinlong Shu, East China Normal University, China

Mathematical Olympiad Series

Vol. 4

Vol. 3

✺ Textbook

4 www.worldscientific.com

• NORTH & SOUTH WorldScientificPublishingCo.Inc. AMERICA 27 Warren Street, Suite 401-402, Hackensack, NJ 07601, USA Toll-free fax: 1 888 977 2665 Toll-free: 1 800 227 7562 Email: sales@wspc.com

• EUROPE&THE World Scientific Publishing (UK) Ltd. MIDDLEEAST c/o Marston Book Services, P O Box 269, Abingdon, Oxon OX14 4YN, UK Fax: 44 (0) 123 546 5555 Tel: 44 (0) 123 546 5500 Email: direct.orders@marston.co.uk

• ASIA&THE WorldScientificPublishingCo.Pte.Ltd. REST OF THE Farrer Road, P O Box 128, SINGAPORE 912805 Fax: 65 6467 7667 Tel: 65 6466 5775 Email: sales@wspc.com.sg WORLD

For orders or enquiries, please contact any of our offices below or visit us at: www.worldscientific.com

SP.TF.05.13.02.HCPrinted in May 2013

* Prices subject to change without prior notice

BESTSELLING TEXTBOOKS

INTRODUCTION TO GRAPH THEORYH3 Mathematicsby Koh Khee Meng (National University of Singapore), Dong Fengming & Tay Eng Guan (Nanyang Technological University, Singapore)

Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college.

The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.

Contents: Fundamental Concepts and Basic Results; Graph Isomorphisms, Subgraphs, the Complement of a Graph; Bipartite Graphs and Trees; Vertex-Colourings of Graphs; Matchings in Bipartite Graphs; Eulerian Multigraphs and Hamiltonian Graphs; Digraphs and Tournaments.

244pp Mar 2007978-981-270-525-9 US$133    £88978-981-270-386-6(pbk) US$83    £55

This is a companion to above book.

260pp Oct 2007978-981-277-175-9(pbk) US$69    £46

CHROMATIC POLYNOMIALS AND CHROMATICITY OF GRAPHSby F M Dong (Nanyang Technological University, Singapore), Koh khee Meng (National University of Singapore) & K L Teo (Massey University, New Zealand)

“This book is clearly written, well illustrated, and supplied with carefully designed exercises, it takes pleasure in using it as an graduate textbook or for independent study. It leads the reader to the frontiers of present research in the theory of chromatic polynomials and offers insight into some exciting development.”

Zentralblatt MATH

This is the first book to comprehensively cover chromatic polynomials of graphs. It includes most of the known results and unsolved problems in the area of chromatic polynomials.

384pp Jun 2005978-981-256-317-0 US$170 £112978-981-256-383-5(pbk) US$91    £60

PRINCIPLES AND TECHNIQUES IN COMBINATORICSby Chen Chuan-Chong & Koh Khee-Meng (National University of Singapore)

“This book should be a must for all mathematicians who are involved in the training of Mathematical Olympiad teams, but it will also be a valuable source of problems for university courses.”

Mathematical Reviews

A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.

Contents: Permutations and Combinations; Binomial Coefficients and Multinomial Coefficients; The Pigeonhole Principle and Ramsey Numbers; The Principle of Inclusion and Exclusion; Generating Functions; Recurrence Relations.

312pp Jul 1992978-981-02-1139-4(pbk) US$39    £26

A FIRST LOOK AT GRAPH THEORYby John Clark & Derek Allan Holton (University of Otago, New Zealand)

This book is intended to be an introductory text for mathematics and computer science students at the second and third year levels in universities. It gives an introduction to the subject with sufficient theory for students at those levels, with emphasis on algorithms and applications.

Contents: An Introduction t o Graphs ; Tr ee s and Connectivity; Euler Tours and Hamiltonian Cycles; Matchings; Planar Graphs; Colouring; Directed Graphs; Networks; Ramsey Theory; Reconstruction.

348pp May 1991978-981-02-0490-7(pbk) US$49    £32

❖ Solution Manual

Essential Titles in Combinatorics & Graph Theory