Combinatorics /
Nicholas A. Loehr
- Second edition
- xxiv, 618 pages ; 27 cm
- Discrete Mathematics And Its Applications .
- Discrete mathematics and its applications .
Previous edition: Bijective combinatorics / Nicholas A. Loehr (Boca Raton, FL : Chapman & Hall/CRC, c2011)
Includes bibliographical references and index
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. --