Colloquium
3:00 p.m., Friday (March 24, 2006)
MATX 1100
Richard Ehrenborg
University of Kentucky
Counting pattern avoiding permutations via integral operators
Abstract: A permutation \pi=(\pi_{1},\ldots,\pi_{n}) is consecutive 123avoiding if there
is no sequence of the form \pi_{i} < \pi_{i+1} < \pi_{i+2}. More generally, for S a
collection of permutations on m+1 elements, this definition extends to define consecutive
Savoiding permutations. We show that the spectrum of an associated integral operator
on the space L^{2}[0,1]^{m} determines the asymptotics of the number of consecutive
Savoiding permutations. Moreover, using an operator version of the classical
FrobeniusPerron theorem due to Krein and Rutman, we prove asymptotic results for
large classes of patterns S. This extends previously known results of Elizalde. This is
joint work with Sergey Kitaev and Peter Perry.
Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).
