We will discuss the combinatorial proof of an identity in Richard Stanley's 'Enumerative Combinatorics: Volume 2'. We will begin by explaining how the identity relates the commutator of a pair of permutations of n elements to a sequence of permutations of a_1, a_2,...,a_k elements; where the a_i sum to n (or to a partitioned permutation of n elements). We will show how to reduce a proof of the identity to a relationship between products of two permutations of the same cycle type with one fixed and partitioned permutations of n elements, and give a natural bijective proof for small values of n.
Graduate Student Combinatorics Seminar
Wednesday, October 29, 2008 - 12:30pm
Paul Levande
University of Pennsylvania