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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 |
Description
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 Enxn⁄n!=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.