UW-PIMS Mathematics Colloquium: Richard Stanley

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≥0Enxnn!=secx+tanx. We will discuss such topics as other occurrences of Euler numbers in mathematics, umbral enumeration of classes of alternating permutations, and longest alternating subsequences of permutations.