Source characterization of the hypergraphic posets

TL;DR

This paper extends the characterization of hypergraphic posets' sources from interval hypergraphs to arbitrary hypergraphs, enhancing understanding of their structure and properties.

Contribution

It generalizes the source characterization of hypergraphic posets from interval hypergraphs to all hypergraphs, broadening the theoretical framework.

Findings

Extended source characterization to arbitrary hypergraphs

Provided new structural insights into hypergraphic posets

Enhanced understanding of hypergraph orientations

Abstract

For a hypergraph $\mathbb{H}$ on $[n]$, the hypergraphic poset $P_\mathbb{H}$ is the transitive closure of the oriented $1$-skeleton of the hypergraphic polytope $\Delta_\mathbb{H}$. In a recent paper, N. Bergeron and V. Pilaud provided a characterization of $P_\mathbb{H}$ based on the sources of acyclic orientations for interval hypergraphs. The goal of this work is to extend this source characterization of $P_\mathbb{H}$ for arbitrary hypergraphs on $[n]$.