A first course in enumerative combinatorics
著者
書誌事項
A first course in enumerative combinatorics
（The Sally series, . Pure and applied undergraduate texts ; 49）
American Mathematical Society, c2020
- : pbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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 Erdo?s number is 2. An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information.
目次
Prologue: Compositions of an integer
Sets, functions, and relations
Binomial coefficients
Multinomial coefficients and ordered partitions
Graphs and trees
Partitions: Stirling, Lah, and cycle numbers
Intermission: Some unifying themes
Combinatorics and number theory
Differences and sums
Enumeration under group actions
Finite vector spaces
Ordered sets
Formal power series
Incidence algebra: The grand unified theory of enumerative combinatorics
Analysis review
Topology review
Abstract algebra review
Index.
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