Enumerative Combinatorics: Volume 1Publisher Description (unedited publisher data) This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference. Library of Congress subject headings for this publication: Combinatorial enumeration problems. |
Contents
II | 1 |
III | 13 |
IV | 17 |
V | 31 |
VI | 40 |
VII | 42 |
IX | 43 |
X | 51 |
XXXI | 126 |
XXXII | 129 |
XXXIII | 131 |
XXXIV | 133 |
XXXV | 135 |
XXXVI | 140 |
XXXVII | 147 |
XXXVIII | 149 |
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Common terms and phrases
a₁ a₂ Amer antichain b₁ b₂ bijection binomial posets boolean algebra c₁ CF(E coefficients Cohen-Macaulay combinatorial proof compute Corollary define denote the number disjoint distributive lattice Enzo equal equation equivalent Eulerian Eulerian posets Example Exercise F₁ finite lattice finite poset finite set formal power series formula function f graded poset graph Hasse diagram Hence instance integer interval isomorphic join-irreducibles Lemma length Let f(n linear matrix maximal chains Möbius function Möbius inversion Möbius inversion formula monoid multiset number of elements number of partitions number of permutations Ō and Ī obtain order ideal order-preserving P-partitions P₁ partially ordered polynomial Principle of Inclusion-Exclusion proof follows Proposition R-labeling rank rational function result rook satisfying semimodular semimodular lattice sequence Show simplicial subposet subsets Suppose Theorem topology unique V₁ vertex vertices x₁ y₁ yields