Title:Source characterization of the hypegraphic posets
| Speaker | Félix Gelinas |
| Affiliation | York |
| Location | MC 5479 |
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 $\Delta_\mathbb{H}$, which is the Minkowski sum of the standard simplices $\Delta_H$ for each hyperedge $H \in \mathbb{H}$. In 2019, C. Benedetti, N. Bergeron, and J. Machacek established a remarkable correspondence between the transitive closure of the oriented $1$-skeleton of $\Delta_\mathbb{H}$ and the flip graph on acyclic orientations of $\mathbb{H}$. Viewing an orientation of $\mathbb{H}$ as a map $A$ from $\mathbb{H}$ to $[n]$, we define the sources of the acyclic orientations as the values $A(H)$ for each hyperedge $H \in \mathbb{H}$. 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. Specifically, two distinct acyclic orientations $A$ and $B$ of $\mathbb{H}$ are comparable in $P_\mathbb{H}$ if and only if their sources satisfy $A(H) \leq B(H)$ for all hyperedges $H\in \HH$. The goal of this work is to extend this source characterization of $P_\mathbb{H}$ to arbitrary hypergraphs on $[n]$.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm,