New recursion formula for the interior polynomial based on non-expanding sets
Combinatorics
2025-06-04 v3 Geometric Topology
Abstract
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 previous work, we derived an alternating cycle recursion formula for the interior polynomial. Here, we introduce a new, more transparent recursion formula based on the structure of non-expanding sets. This formula offers a clearer combinatorial interpretation of the interior polynomial and its connection to polyhedral geometry.
Cite
@article{arxiv.2502.19799,
title = {New recursion formula for the interior polynomial based on non-expanding sets},
author = {Keiju Kato},
journal= {arXiv preprint arXiv:2502.19799},
year = {2025}
}
Comments
13pages, 11figures, 2tables