Enumerative Combinatorics: Volume 1

Enumerative Combinatorics: Volume 1
Author :
Publisher : Cambridge University Press
Total Pages : 641
Release :
ISBN-10 : 9781107015425
ISBN-13 : 1107015421
Rating : 4/5 (25 Downloads)

Synopsis Enumerative Combinatorics: Volume 1 by : Richard P. Stanley

Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.

Counting: The Art of Enumerative Combinatorics

Counting: The Art of Enumerative Combinatorics
Author :
Publisher : Springer Science & Business Media
Total Pages : 263
Release :
ISBN-10 : 9781475748789
ISBN-13 : 1475748787
Rating : 4/5 (89 Downloads)

Synopsis Counting: The Art of Enumerative Combinatorics by : George E. Martin

This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.

Enumerative Combinatorics: Volume 2

Enumerative Combinatorics: Volume 2
Author :
Publisher : Cambridge University Press
Total Pages : 600
Release :
ISBN-10 : 0521789877
ISBN-13 : 9780521789875
Rating : 4/5 (77 Downloads)

Synopsis Enumerative Combinatorics: Volume 2 by : Richard P. Stanley

An introduction, suitable for beginning graduate students, showing connections to other areas of mathematics.

Handbook of Enumerative Combinatorics

Handbook of Enumerative Combinatorics
Author :
Publisher : CRC Press
Total Pages : 1073
Release :
ISBN-10 : 9781482220865
ISBN-13 : 1482220865
Rating : 4/5 (65 Downloads)

Synopsis Handbook of Enumerative Combinatorics by : Miklos Bona

Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.This important new work is edited by Miklos Bona of the University of Florida where he

A First Course in Enumerative Combinatorics

A First Course in Enumerative Combinatorics
Author :
Publisher : American Mathematical Soc.
Total Pages : 272
Release :
ISBN-10 : 9781470459956
ISBN-13 : 1470459957
Rating : 4/5 (56 Downloads)

Synopsis A First Course in Enumerative Combinatorics by : Carl G. Wagner

A First Course in Enumerative Combinatorics provides an introduction to the fundamentals of enumeration for advanced undergraduates and beginning graduate students in the mathematical sciences. The book offers a careful and comprehensive account of the standard tools of enumeration—recursion, generating functions, sieve and inversion formulas, enumeration under group actions—and their application to counting problems for the fundamental structures of discrete mathematics, including sets and multisets, words and permutations, partitions of sets and integers, and graphs and trees. The author's exposition has been strongly influenced by the work of Rota and Stanley, highlighting bijective proofs, partially ordered sets, and an emphasis on organizing the subject under various unifying themes, including the theory of incidence algebras. In addition, there are distinctive chapters on the combinatorics of finite vector spaces, a detailed account of formal power series, and combinatorial number theory. The reader is assumed to have a knowledge of basic linear algebra and some familiarity with power series. There are over 200 well-designed exercises ranging in difficulty from straightforward to challenging. There are also sixteen large-scale honors projects on special topics appearing throughout the text. The author is a distinguished combinatorialist and award-winning teacher, and he is currently Professor Emeritus of Mathematics and Adjunct Professor of Philosophy at the University of Tennessee. He has published widely in number theory, combinatorics, probability, decision theory, and formal epistemology. His Erdős number is 2.

Analytic Combinatorics in Several Variables

Analytic Combinatorics in Several Variables
Author :
Publisher : Cambridge University Press
Total Pages : 395
Release :
ISBN-10 : 9781107031579
ISBN-13 : 1107031575
Rating : 4/5 (79 Downloads)

Synopsis Analytic Combinatorics in Several Variables by : Robin Pemantle

Aimed at graduate students and researchers in enumerative combinatorics, this book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective.

Algebraic Combinatorics

Algebraic Combinatorics
Author :
Publisher : Springer Science & Business Media
Total Pages : 226
Release :
ISBN-10 : 9781461469988
ISBN-13 : 1461469988
Rating : 4/5 (88 Downloads)

Synopsis Algebraic Combinatorics by : Richard P. Stanley

Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.

Combinatorics: The Art of Counting

Combinatorics: The Art of Counting
Author :
Publisher : American Mathematical Soc.
Total Pages : 304
Release :
ISBN-10 : 9781470460327
ISBN-13 : 1470460327
Rating : 4/5 (27 Downloads)

Synopsis Combinatorics: The Art of Counting by : Bruce E. Sagan

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.

A Course in Enumeration

A Course in Enumeration
Author :
Publisher : Springer Science & Business Media
Total Pages : 568
Release :
ISBN-10 : 9783540390350
ISBN-13 : 3540390359
Rating : 4/5 (50 Downloads)

Synopsis A Course in Enumeration by : Martin Aigner

Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. There are 666 exercises, and every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.

Catalan Numbers

Catalan Numbers
Author :
Publisher : Cambridge University Press
Total Pages : 225
Release :
ISBN-10 : 9781107075092
ISBN-13 : 1107075092
Rating : 4/5 (92 Downloads)

Synopsis Catalan Numbers by : Richard P. Stanley

Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. Following an introduction to the basic properties of Catalan numbers, the book presents 214 different kinds of objects counted by them in the form of exercises with solutions. The reader can try solving the exercises or simply browse through them. Some 68 additional exercises with prescribed difficulty levels present various properties of Catalan numbers and related numbers, such as Fuss-Catalan numbers, Motzkin numbers, Schröder numbers, Narayana numbers, super Catalan numbers, q-Catalan numbers and (q,t)-Catalan numbers. The book ends with a history of Catalan numbers by Igor Pak and a glossary of key terms. Whether your interest in mathematics is recreation or research, you will find plenty of fascinating and stimulating facts here.