Intervals and factors in the Bruhat order

Bridget Eileen Tenner

Published 2013-03-15, updated 2015-05-28Version 2

In this paper we study those generic intervals in the Bruhat order of the symmetric group that are isomorphic to the principal order ideal of a permutation w, and consider when the minimum and maximum elements of those intervals are related by a certain property of their reduced words. We show that the property does not hold when w is a decomposable permutation, and that the property always holds when w is the longest permutation.