Geometric view of interval poset permutations

Abstract

In a recent study by Tenner, the concept of the interval poset of a permutation was introduced to effectively represent all intervals and their inclusions within a permutation. In this paper, we present a new geometric viewpoint on interval posets. We establish a one-to-one correspondence between the set of interval posets for permutations of size n and a specific subset of dissections of a convex polygon with n sides. Through this correspondence, we investigate various intriguing subsets of interval posets and uncover their connections with specific polygon dissections.