Geometric view of interval poset permutations
Combinatorics
2025-09-30 v3
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.
Cite
@article{arxiv.2411.13193,
title = {Geometric view of interval poset permutations},
author = {Eli Bagno and Estrella Eisenberg and Shulamit Reches and Moriha Sigron},
journal= {arXiv preprint arXiv:2411.13193},
year = {2025}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2406.16392