Combinatorics Discrete Mathematics and its Applications 2nd Edition by Nicholas Loehr ISBN 1498780253 978-1498780254

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Product details: 

ISBN 10:1498780253

ISBN 13:978-1498780254

Author:Nicholas Loehr

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

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Tags: Nicholas Loehr, Combinatorics, Discrete, Mathematics