Combinatorial EnumerationThis 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. |
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₁-strings a₁ alternating permutations altitude b₁ branch decomposition c₁ circular permutations coefficients combinatorial composition configurations consider cycle d₁ denote distinguished Durfee square element enumeration example exponential generating function f₁ Ferrers graph formal power series functional equation gives i₁ integers inversions k-subsets k₁ L₁ labeled trees Lagrange theorem left-most lemma length M₁ marking matrix maximal blocks maximal string decomposition monovalent vertices N₁ near-triangulations nonroot vertices number of partitions number of permutations number of sequences obtain ordered partition ordinary generating function outer face P₁ plane partitions planted plane trees polynomial power series product lemma R₁ recurrence equation required number respect result follows root edge rooted planar maps s-objects Show step-set string decomposition theorem subsets substrings t₁ tagged trace log(I transformation lemma unique v₁ vertex w₁ weighted path x₁ y₁ α₁ π₁ πι σ₁ σι