Two Posets of Noncrossing Partitions Coming From Undesired Parking Spaces

Consider the noncrossing set partitions of an n-element set which, either do not use the block {n - 1, n} or which do not use both the singleton block {n} and a block containing 1 and n - 1. In this article we study the subposet of the noncrossing partition lattice induced by these elements, and sho...