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arXiv · 2411.13193

Geometric view of interval poset permutations

Eli Bagno·Estrella Eisenberg·Shulamit Reches·Moriha Sigron
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Abstract

In a recent study, Tenner introduced the concept of the interval poset of a permutation 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 $n+1$ sides. Through this correspondence, we investigate various intriguing subsets of interval posets and uncover their connections with specific polygon dissections.

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Eli Bagno, Estrella Eisenberg, Shulamit Reches, Moriha Sigron. 2026-08-31. Geometric view of interval poset permutations. https://arxiv.org/abs/2411.13193

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