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<p>We study the difference between the number of facets of the order polytope and the chain polytope of a poset. Hibi and Li classified posets where the gap is exactly zero. We describe the bounds on this gap using the new notion of crossing numbers, and then use this result to classify the posets where the gap is exactly one.</p>

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Gap Between the Number of Facets of the Two Poset Polytopes

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年8月1日

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  • Binaya Bhandari,
  • Debra Cunningham,
  • Grace Morrell,
  • SuHo Oh,
  • Paxton Smith

摘要

We study the difference between the number of facets of the order polytope and the chain polytope of a poset. Hibi and Li classified posets where the gap is exactly zero. We describe the bounds on this gap using the new notion of crossing numbers, and then use this result to classify the posets where the gap is exactly one.