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An Invitation to Combinatorics

An Invitation to Combinatorics PDF Author: Shahriar Shahriari
Publisher: Cambridge University Press
ISBN: 1108476546
Category : MATHEMATICS
Languages : en
Pages : 631
Book Description
A conversational introduction to combinatorics for upper undergraduates, emphasizing problem solving and active student participation.

An Invitation to Combinatorics

An Invitation to Combinatorics PDF Author: Shahriar Shahriari
Publisher: Cambridge University Press
ISBN: 1108476546
Category : MATHEMATICS
Languages : en
Pages : 631
Book Description
A conversational introduction to combinatorics for upper undergraduates, emphasizing problem solving and active student participation.

An Invitation to Analytic Combinatorics

An Invitation to Analytic Combinatorics PDF Author: Stephen Melczer
Publisher: Springer Nature
ISBN: 3030670805
Category : Mathematics
Languages : en
Pages : 418
Book Description
This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.

Surveys in Combinatorics 2021

Surveys in Combinatorics 2021 PDF Author: Konrad K. Dabrowski
Publisher: Cambridge University Press
ISBN: 1009018884
Category : Mathematics
Languages : en
Pages : 379
Book Description
These nine articles provide up-to-date surveys of topics of contemporary interest in combinatorics.

An Invitation to Pursuit-Evasion Games and Graph Theory

An Invitation to Pursuit-Evasion Games and Graph Theory PDF Author: Anthony Bonato
Publisher: American Mathematical Society
ISBN: 1470467631
Category : Mathematics
Languages : en
Pages : 254
Book Description
Graphs measure interactions between objects such as friendship links on Twitter, transactions between Bitcoin users, and the flow of energy in a food chain. While graphs statically represent interacting systems, they may also be used to model dynamic interactions. For example, imagine an invisible evader loose on a graph, leaving only behind breadcrumb clues to their whereabouts. You set out with pursuers of your own, seeking out the evader's location. Would you be able to detect their location? If so, then how many resources are needed for detection, and how fast can that happen? These basic-seeming questions point towards the broad conceptual framework of pursuit-evasion games played on graphs. Central to pursuit-evasion games on graphs is the idea of optimizing certain parameters, whether they are the cop number, burning number, or localization number, for example. This book would be excellent for a second course in graph theory at the undergraduate or graduate level. It surveys different areas in graph searching and highlights many fascinating topics intersecting classical graph theory, geometry, and combinatorial designs. Each chapter ends with approximately twenty exercises and five larger scale projects.

Analytic Combinatorics

Analytic Combinatorics PDF Author: Philippe Flajolet
Publisher: Cambridge University Press
ISBN: 1139477161
Category : Mathematics
Languages : en
Pages :
Book Description
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes

Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes PDF Author: Hibi Takayuki
Publisher: World Scientific
ISBN: 9811200491
Category : Mathematics
Languages : en
Pages : 476
Book Description
This volume consists of research papers and expository survey articles presented by the invited speakers of the Summer Workshop on Lattice Polytopes. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further developments of many research areas surrounding this field. With the survey articles, research papers and open problems, this volume provides its fundamental materials for graduate students to learn and researchers to find exciting activities and avenues for further exploration on lattice polytopes.

Combinatorial Reciprocity Theorems: An Invitation to Enumerative Geometric Combinatorics

Combinatorial Reciprocity Theorems: An Invitation to Enumerative Geometric Combinatorics PDF Author: Matthias Beck
Publisher: American Mathematical Soc.
ISBN: 147042200X
Category : Combinatorial analysis
Languages : en
Pages : 308
Book Description
Combinatorial reciprocity is a very interesting phenomenon, which can be described as follows: A polynomial, whose values at positive integers count combinatorial objects of some sort, may give the number of combinatorial objects of a different sort when evaluated at negative integers (and suitably normalized). Such combinatorial reciprocity theorems occur in connections with graphs, partially ordered sets, polyhedra, and more. Using the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics. Written in a friendly writing style, this is an accessible graduate textbook with almost 300 exercises, numerous illustrations, and pointers to the research literature. Topics include concise introductions to partially ordered sets, polyhedral geometry, and rational generating functions, followed by highly original chapters on subdivisions, geometric realizations of partially ordered sets, and hyperplane arrangements.

Combinatorics: The Art of Counting

Combinatorics: The Art of Counting PDF Author: Bruce E. Sagan
Publisher: American Mathematical Soc.
ISBN: 1470460327
Category : Education
Languages : en
Pages : 304
Book Description
This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Combinatorial Methods with Computer Applications

Combinatorial Methods with Computer Applications PDF Author: Jonathan L. Gross
Publisher: CRC Press
ISBN: 1584887443
Category : Computers
Languages : en
Pages : 664
Book Description
Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinat

Combinatorial Algorithms

Combinatorial Algorithms PDF Author: Donald L. Kreher
Publisher: CRC Press
ISBN: 1000102874
Category : Mathematics
Languages : en
Pages : 344
Book Description
This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as: Combinations Permutations Graphs Designs Many classical areas are covered as well as new research topics not included in most existing texts, such as: Group algorithms Graph isomorphism Hill-climbing Heuristic search algorithms This work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area. The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, electrical engineering, and computer science can understand without needing a prior course on combinatorics.