# Combinatorics Seminar- Permuted Packings and Permutation Breadth

Speaker: Cheyne Homberger, UMBC
Date and time: Thursday, November 8, 4-5pm
Place:  Phillips 110
Title: Permuted Packings and Permutation Breadth

Abstract: The breadth of a permutation π is the minimum value of |i - j| + |π(i) - π(j)|, taken over all relevant i and j. Breadth has important consequences to permutation pattern containment, and connections to plane tiling.  In this talk we explore the breadth of random permutations using both probabilistic techniques and combinatorial geometry.  In particular, we present the expected breadth of a random permutation, the proportion of permutations with a fixed breadth, and a constructive proof for maximizing unique large patterns in permutations.  This talk is based on work with both David Bevan and Bridget Tenner and with Simon Blackburn and Pete Winkler.