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math.CO2024
Equivariant Ehrhart Theory of Hypersimplices
Oliver Clarke, Max Kölbl
We study the hypersimplex under the action of the symmetric group by coordinate permutation. We prove that the evaluation of its equivariant -polynomial at is the pe…
math.CO2024
On a Conjecture Concerning the Roots of Ehrhart Polynomials of Symmetric Edge Polytopes from Complete Multipartite Graphs
Max Kölbl
In [7], Higashitani, Kummer, and Michałek pose a conjecture about the symmetric edge polytopes of complete multipartite graphs and confirm it for a number of families in the bipart…
math.CO2024
Diameter reduction via arc reversal
Panna Gehér, Max Kölbl, Lydia Mirabel Mendoza-Cadena +1
The diameter of a directed graph is the maximum distance between any pair of vertices. We study a problem that generalizes \textsc{Oriented Diameter}: For a given directed graph an…