Noncrossing and Nonnesting Partitions for Parabolic Quotients

Recent work has joined two threads in algebraic combinatorics. The first is that reduced words for the longest element in type A are in bijection with staircase standard Young tableaux, and the second is that there are the same number of noncrossing and nonnesting partitions in any type. The relation between reduced words and standard Young tableaux is not limited to the longest element; we exploit this and other machinery to define reasonable analogues of noncrossing and nonnesting partitions for parabolic quotients in type A.