CiNii Books - Combinatorics

Author(s)

- Loehr, Nicholas A.

Bibliographic Information

Combinatorics

Nicholas A. Loehr

（Discrete mathematics and its applications / Kenneth H. Rosen, series editor）

CRC Press, c2018

2nd ed

: hardback

Available at / 3 libraries

Osaka University, Main Library

: hardback12200319999

OPAC
Science and Technology Library, Kyushu University

: hardbackLOEH/10/2033212017003592

OPAC
東京大学数理科学研究科図書

: hardbackFU:Loehr:N.8010705153

OPAC
No Libraries matched.
Remove all filters.

Search this Book/Journal

Note

"A Chapman & Hall book"

Includes bibliographical references (p. 595-601) and index

Description and Table of Contents

Description

Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics. This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.

Table of Contents

PART 1: ENUMERATION. Chapter 1: Basic Counting
Chapter 2: Combinatorial Identities and Recursions
Chapter 3: Counting Problems in Graph Theory
Chapter 4: Inclusion-Exclusion and Related Techniques
New Chapter 5: Generating Functions
Chapter 6: Ranking, Unranking, and Successor Algorithms
PART 2: ALGEBRAIC COMBINATORICS
Chapter 7: Permutation Statistics and q-Analogues
Chapter 8: Permutations and Group Actions
Chapter 9: Tableaux and Symmetric Polynomials. Chapter 10: Abaci and Antisymmetric Polynomials
Chapter 11: Additional Topics. New Appendix: Background in Abstract Algebra.

by "Nielsen BookData"