• 1 Department of Mathematical Sciences [Chicago]

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.

• 05C69 - Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
• 90C05 - Linear programming