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A survey of alternating permutations

Colloquium

Speaker: Richard Stanley, MIT
Location: 1147 MSB
Start time: Mon, Jan 11 2010, 5:30PM

An alternating permutation w=a1 ... an of 1,2,...,n is a permutation such that ai>ai+1 if and only if i is odd. If En (called an Euler number) denotes the number of alternating permutations of 1,2,...,n, then ∑n ≥ 0 Enxnn!=sec x+tan x. We will discuss such topics as other occurrences of Euler numbers in mathematics, umbral enumeration of classes of alternating permutations, longest alternating subsequences of permutations, and a connection with a noncommutative polynomial called the cd-index of the symmetric group.