Colloquium ICJ

(Cyclically) consecutive 123-avoiding permutations

by Richard Ehrenborg (University of Kentucky)

Europe/Paris
Salle Fokko (UCBL-Braconnier)

Salle Fokko

UCBL-Braconnier

21 av Claude Bernard, 69100 VILLEURBANNE
Description
A permutation pi=(pi_1,...,pi_n) is consecutive 123-avoiding if there is no index i such that pi_i < pi_{i+1} < pi_{i+2}. Similarly, a permutation pi is cyclically consecutive 123-avoiding if the indices are viewed modulo n. These two definitions extend to (cyclically) consecutive S-avoiding permutations, where S is some collection of permutations on m+1 elements. We determine the asymptotic behavior for the number of consecutive 123-avoiding permutations by studying an operator on the space L^2([0,1]^2). In fact, we obtain an asymptotic expansion for this number. Furthermore we obtain an exact expression for the number of cyclically consecutive 123-avoiding permutations. A few results will be stated about the general case of (cyclically) consecutive S-avoiding permutations. Part of these results are joint work with Sergey Kitaev and Peter Perry. The talk will be aimed at a general mathematical audience.