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<p>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.</p>

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New recursion formula for the interior polynomial based on non-expanding sets

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Keiju Kato

摘要

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.