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Combinatorics / Nicholas A. Loehr.

By: Material type: TextTextSeries: Discrete mathematics and its applicationsPublication details: Boca Raton : CRC Press, ©2018.Edition: Second editionDescription: xxiv, 618 pages : illustrations ; 27 cmISBN:
  • 9781498780254
Subject(s): DDC classification:
  • 511.62 23 L825
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: Groups, Permutations, and Group Actions; Chapter 8: Permutation Statistics and q-Analogues; Chapter 9: Tableaux and Symmetric Polynomials. Chapter 10: Abaci and Antisymmetric Polynomials; Chapter 11: Algebraic Aspects of Generating functions; Chapter 12: Additional Topics. New Appendix: Background in Abstract Algebra.
Summary: Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, the book presents an introduction to enumerative and algebraic combinatorics emphasizing bijective methods. The text develops mathematical tools, such as basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear-algebraic methods to solve enumeration problems. The tools are used to analyze combinatorial structures, words, permutations, subsets, functions, compositions, integer partitions, graphs, trees, lattice paths, multisets, rook placements, and set partitions. --
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 511.62 L825 (Browse shelf(Opens below)) Available 138379
Total holds: 0

Includes bibliographical references and index.

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: Groups, Permutations, and Group Actions; Chapter 8: Permutation Statistics and q-Analogues; Chapter 9: Tableaux and Symmetric Polynomials. Chapter 10: Abaci and Antisymmetric Polynomials; Chapter 11: Algebraic Aspects of Generating functions; Chapter 12: Additional Topics. New Appendix: Background in Abstract Algebra.

Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, the book presents an introduction to enumerative and algebraic combinatorics emphasizing bijective methods. The text develops mathematical tools, such as basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear-algebraic methods to solve enumeration problems. The tools are used to analyze combinatorial structures, words, permutations, subsets, functions, compositions, integer partitions, graphs, trees, lattice paths, multisets, rook placements, and set partitions. --

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