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math.CO2025
New recursion formula for the interior polynomial based on non-expanding sets
Keiju Kato
The interior polynomial was originally defined for hypergraphs and later shown to coincide with the Ehrhart polynomial of the root polytope of an associated bipartite graph. In pre…
math.CO2019
The Hopf monoid and the basic invariant of directed graphs
Keiju Kato
Aguiar and Ardila defined the Hopf monoid GP of generalized permutahedra and showed that it contains many submonoids that correspond to combinatorial objects. They also give a basi…
math.CO2018
A mirroring formula for the interior polynomial of a bipartite graph
Keiju Kato
The interior polynomial is an invariant of (signed) bipartite graphs, and the interior polynomial of a plane bipartite graph is equal to a part of the HOMFLY polynomial of a natura…