Partitions, permutations and posets
نویسنده
چکیده
1. Partitions For the definition of (number) partition, Ferrers diagram and Young tableaux, conjugate partition see Chapter 6 of R. Stanley’s Algebraic Combinatorics book. This section is based (more or less) on the treatment of the book A Course in Combinatorics by Van Lint and Wilson (Chapter 15). Proposition 1.1. Let pk(n) be the number of partitions of n into at most k parts. Let p(n) be the number of partitions of n with at most k parts. Then pk(n) = p (n). Proof. There is a natural bijection between the two sets: associate the conjugate partition to a partition. Next let us understand the generating function of the sequence (pk(n)). Theorem 1.2. We have ∞ ∑
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تاریخ انتشار 2016