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An overview of all enumerative combinatorics within reach of undergraduates; the two fundamental themes of bijective proofs and generating functions, together with their intimate connections, recur constantly. A wide selection of topics, including several never appearing before …
Combinatorial games -- Basic techniques -- Outcome classes -- Motivational interlude -- The Algebra of games -- Values of games -- Structure -- Impartial games -- Hot games -- All-small games -- Omega.
Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations. The presentation prioritizes elementary enumerative proofs. Therefore, parts of the book are designed s…