This graduate-level text presents an encyclopedic account of the mathematical theory and problem-solving techniques associated with enumeration problems. Its approach blends combinatorial and algebraic ideas to offer insights into a wide variety of problems, and each section of the book focuses on a specific discrete structure, advancing from elementary (often classical) results to those at research level. Subjects include the combinatorics of the ordinary generating function and the exponential generating function, the combinatorics of sequences, and the combinatorics of paths. The text is complemented by approximately 350 exercises with full solutions. 1983 edition. Foreword by Gian-Carlo Rota. References. Index.
adjacent alternating permutations altitude branch decomposition circular permutations coefficients combinatorial composition configurations consider construction contains corresponding cycles Definition degree deleted differential equation distinct Durfee square element enumeration example exponential generating function Ferrers graph formal power series functional equation given gives identity integers k-subsets labeled graphs labeled trees Lagrange theorem left-most path linear marking matrix maximal blocks maximal string decomposition monovalent vertices nonempty nonroot vertices nonseparable rooted planar number of edges number of partitions number of permutations number of sequences obtain occurrences ordered partition ordinary generating function outer face pair pattern plane partitions planted plane trees polynomial problem product lemma Proof Proposition q-analogue recurrence equation required generating function required number respect result follows root edge root vertex rooted planar maps rows and columns s-objects s-tagged sequences of type Show solution step-set string decomposition theorem subsets tagged objects tion transformation lemma unique vertex weighted path