# Events

## (Cyclically) consecutive 123-avoiding permutations

### Richard Ehrenborg

University of Kentucky

Barton Lectures in Computational Mathematics

### When

Date: Friday, November 8, 2019

Time: 4:00 pm - 5:00 pm

Location: Petty 150

A permutation =(_{1},…,_{n}) is consecutive 123-avoiding if there is no index such that _{𝑖} < _{𝑖}_{+1} < _{𝑖}_{+2}. Similarly, a permutation π 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.