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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-felix
SUMMARY:Algebraic and enumerative combinatorics seminar-Félix Gelinas
CLASS:PUBLIC
DESCRIPTION:TITLE:Source characterization of the hypegraphic posets\n\nSpea
 ker\n Félix Gelinas\n\nAffiliation\n York\n\nLocation\n MC 5479\n\nABSTR
 ACT: For a hypergraph $\\mathbb{H}$ on $[n]$\, the hypergraphic\nposet $P_
 \\mathbb{H}$ is the transitive closure of the oriented\n$1$-skeleton of th
 e hypergraphic polytope $\\Delta_\\mathbb{H}$\, which\nis the Minkowski su
 m of the standard simplices $\\Delta_H$ for each\nhyperedge $H \\in \\math
 bb{H}$. In 2019\, C. Benedetti\, N. Bergeron\, and\nJ. Machacek establishe
 d a remarkable correspondence between the\ntransitive closure of the orien
 ted $1$-skeleton of $\\Delta_\\mathbb{H}$\nand the flip graph on acyclic o
 rientations of $\\mathbb{H}$. Viewing an\norientation of $\\mathbb{H}$ as 
 a map $A$ from $\\mathbb{H}$ to $[n]$\,\nwe define the sources of the acyc
 lic orientations as the values $A(H)$\nfor each hyperedge $H \\in \\mathbb
 {H}$. In a recent paper\, N. Bergeron\nand V. \n\nPilaud provided a charac
 terization of $P_\\mathbb{H}$ based on the\nsources of acyclic orientation
 s for interval hypergraphs.\nSpecifically\, two distinct acyclic orientati
 ons $A$ and $B$ of\n$\\mathbb{H}$ are comparable in $P_\\mathbb{H}$ if and
  only if their\nsources satisfy $A(H) \\leq B(H)$ for all hyperedges $H\\i
 n \\HH$. The\ngoal of this work is to extend this source characterization 
 of\n$P_\\mathbb{H}$ to arbitrary hypergraphs on $[n]$.\n\nTHERE WILL BE A 
 PRE-SEMINAR PRESENTING RELEVANT BACKGROUND AT THE\nBEGINNING GRADUATE LEVE
 L STARTING AT 1:30PM\,
DTSTAMP:20260403T081438Z
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