Universal Cycles for K-subsets of an N-set PDF Download

Author: Melinda Lanius
Publisher:
ISBN:
Category : Algebraic cycles
Languages : en
Pages :

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Book Description
Generalized from the classic de Bruijn sequence, a universal cycle is a compact cyclic list of information. Existence of universal cycles has been established for a variety of families of combinatorial structures. These results, by encoding each object within a combinatorial family as a length-j word, employ a modified version of the de Bruijn graph to establish a correspondence between an Eulerian circuit and a universal cycle. We explore the existence of universal cycles for k-subsets of the integers {1, 2 ..., n}. The fact that sets are unordered seems to prevent the use of the established encoding techniques used in proving existence. We explore this difficulty and introduce an intermediate step that may allow us to use the familiar encoding and correspondence to prove existence. Moreover, mathematicians Persi Diaconis and Ron Graham hold that "the construction of universal cycles has proceeded by clever, hard, ad-hoc arguments" and that no general theory exists. Accordingly, our work pushes for a more general approach that can inform other universal cycle problems.

Author: Fan Chung
Publisher: CRC Press
ISBN: 1000752097
Category : Mathematics
Languages : en
Pages : 386

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Book Description
50 Years of Combinatorics, Graph Theory, and Computing advances research in discrete mathematics by providing current research surveys, each written by experts in their subjects. The book also celebrates outstanding mathematics from 50 years at the Southeastern International Conference on Combinatorics, Graph Theory & Computing (SEICCGTC). The conference is noted for the dissemination and stimulation of research, while fostering collaborations among mathematical scientists at all stages of their careers. The authors of the chapters highlight open questions. The sections of the book include: Combinatorics; Graph Theory; Combinatorial Matrix Theory; Designs, Geometry, Packing and Covering. Readers will discover the breadth and depth of the presentations at the SEICCGTC, as well as current research in combinatorics, graph theory and computer science. Features: Commemorates 50 years of the Southeastern International Conference on Combinatorics, Graph Theory & Computing with research surveys Surveys highlight open questions to inspire further research Chapters are written by experts in their fields Extensive bibliographies are provided at the end of each chapter

Author: Megan Dewar
Publisher: Springer Science & Business Media
ISBN: 1461443253
Category : Mathematics
Languages : en
Pages : 219

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Book Description
The study of combinatorial block designs is a vibrant area of combinatorial mathematics with connections to finite geometries, graph theory, coding theory and statistics. The practice of ordering combinatorial objects can trace its roots to bell ringing which originated in 17th century England, but only emerged as a significant modern research area with the work of F. Gray and N. de Bruijn. These two fascinating areas of mathematics are brought together for the first time in this book. It presents new terminology and concepts which unify existing and recent results from a wide variety of sources. In order to provide a complete introduction and survey, the book begins with background material on combinatorial block designs and combinatorial orderings, including Gray codes -- the most common and well-studied combinatorial ordering concept -- and universal cycles. The central chapter discusses how ordering concepts can be applied to block designs, with definitions from existing (configuration orderings) and new (Gray codes and universal cycles for designs) research. Two chapters are devoted to a survey of results in the field, including illustrative proofs and examples. The book concludes with a discussion of connections to a broad range of applications in computer science, engineering and statistics. This book will appeal to both graduate students and researchers. Each chapter contains worked examples and proofs, complete reference lists, exercises and a list of conjectures and open problems. Practitioners will also find the book appealing for its accessible, self-contained introduction to the mathematics behind the applications.

Author: Thierry Lecroq
Publisher: Springer
ISBN: 3642452787
Category : Computers
Languages : en
Pages : 494

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Book Description
This book constitutes the thoroughly refereed post-workshop proceedings of the 24th International Workshop on Combinatorial Algorithms, IWOCA 2013, held in Rouen, France, in July 2013. The 33 revised full papers presented together with 10 short papers and 5 invited talks were carefully reviewed and selected from a total of 91 submissions. The papers are organized in topical sections on algorithms on graphs; algorithms on strings; discrete geometry and satisfiability.

Author: Konrad K. Dabrowski
Publisher: Cambridge University Press
ISBN: 1009041819
Category : Mathematics
Languages : en
Pages : 380

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Book Description
This volume contains nine survey articles based on plenary lectures given at the 28th British Combinatorial Conference, hosted online by Durham University in July 2021. This biennial conference is a well-established international event, attracting speakers from around the world. Written by some of the foremost researchers in the field, these surveys provide up-to-date overviews of several areas of contemporary interest in combinatorics. Topics discussed include maximal subgroups of finite simple groups, Hasse–Weil type theorems and relevant classes of polynomial functions, the partition complex, the graph isomorphism problem, and Borel combinatorics. Representing a snapshot of current developments in combinatorics, this book will be of interest to researchers and graduate students in mathematics and theoretical computer science.

Author: Erik D. Demaine
Publisher: CRC Press
ISBN: 143986571X
Category : Mathematics
Languages : en
Pages : 361

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Book Description
Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler. And of course there is something from the original puzzlemaster himself, Martin Gardner.

Author: My T. Thai
Publisher: Springer
ISBN: 3642140319
Category : Computers
Languages : en
Pages : 553

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Book Description
This book constitutes the proceedings of the 16th Annual International Conference on Computing and Combinatorics, held in Nha Trang, Vietnam, in July 2010.

Author: Ersébet Csuhaj-Varjú
Publisher: Springer
ISBN: 3662445220
Category : Computers
Languages : en
Pages : 584

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Book Description
This two volume set LNCS 8634 and LNCS 8635 constitutes the refereed conference proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014, held in Budapest, Hungary, in August 2014. The 95 revised full papers presented together with 6 invited talks were carefully selected from 270 submissions. The focus of the conference was on following topics: Logic, Semantics, Automata, Theory of Programming, Algorithms, Complexity, Parallel and Distributed Computing, Quantum Computing, Automata, Grammars and Formal Languages, Combinatorics on Words, Trees and Games.

Author: Persi Diaconis
Publisher: Princeton University Press
ISBN: 0691169772
Category : Crafts & Hobbies
Languages : en
Pages : 258

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Book Description
"Magical Mathematics reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge. For example, the Gilbreath principle--a fantastic effect where the cards remain in control despite being shuffled--is found to share an intimate connection with the Mandelbrot set. Other card tricks link to the mathematical secrets of combinatorics, graph theory, number theory, topology, the Riemann hypothesis, and even Fermat's last theorem. Diaconis and Graham are mathematicians as well as skilled performers with decades of professional experience between them. In this book they share a wealth of conjuring lore, including some closely guarded secrets of legendary magicians. Magical Mathematics covers the mathematics of juggling and shows how the I Ching connects to the history of probability and magic tricks both old and new. It tells the stories--and reveals the best tricks--of the eccentric and brilliant inventors of mathematical magic. Magical Mathematics exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card monte, traces the history of mathematical magic back to the thirteenth century and the oldest mathematical trick--and much more"-

Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 892

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