English

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.

Keywords

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

R2 v1 2026-06-28T21:59:42.098Z