Introduction to Enumerative Combinatorics
Written by one of the leading authors and researchers in the field, this comprehensive modern text offers a strong focus on enumeration, a vitally important area in introductory combinatorics crucial for further study in the field. Miklós Bóna's text fills the gap between introductory textbooks in discrete mathematics and advanced graduate textbooks in enumerative combinatorics, and is one of the very first intermediate-level books to focus on enumerative combinatorics. The text can be used for an advanced undergraduate course by thoroughly covering the chapters in Part I on basic enumeration and by selecting a few special topics, or for an introductory graduate course by concentrating on the main areas of enumeration discussed in Part II. The special topics of Part III make the book suitable for a reading course.
This text is part of the Walter Rudin Student Series in Advanced Mathematics.
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Direct Applications of Basic Methods
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assume bijection binomial coefficients blocks boxes called Chapter choose claim codewords color column combinatorial compute contain cycle cycle notation defined definition digits disjoint divisible entries equal exactly Example explicit formula exponential generating function Ferrers shape finite projective plane fixed formal power series graph G Hn(r hypergraph identical Inclusion-Exclusion Principle induced subgraph induction inequality intersection inversions labeled least left-hand side Lemma Let G line sum log-concave magic cubes magic square matrix multiset nonnegative integers northeastern lattice paths Note number of edges number of partitions number of possibilities ordinary generating function pair parking function permutation matrices Pigeonhole Principle plane trees polynomial positive integers previous exercise problem Product Formula proof Proposition prove real numbers result right-hand side rooted forests rooted plane trees rooted trees satisfying shown in Figure shows side counts Solution Stirling numbers subgraph subsets Subtraction Principle symmetric Theorem total number vertex set vertices