Dr. Paul Horn
University of Denver
Talk is at 11:00 AM Central Time (calculating your local time…)
Abstract
The weak and strong Bruhat orders are fundamental objects in algebraic combinatorics. Both are partial orders on the symmetric group — that is the set of permutations on [n] letters — and can be relatively simply defined in terms of properties of the permutations themselves. Despite their central role — with connections to many combinatorial and representation theoretical objects — there are many basic questions about them that are not fully understood. Indeed, even the extremely natural problem of determining how many pairs of permutations they compare is not fully understood.
In this talk we’ll discuss recent improvements to estimates on this number of pairs, improving results of Hammett and Pittel from 20 years ago. Along the way, we’ll connect this problem to many areas: Young Tableau via the RSK algorithm, the longest-increasing-subsequence problem in permutations, and the behavior of random walks on Z.