超立方体与结合多面体之间的组合插值
A combinatorial interpolation between the hypercube and the associahedron
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中文总结 AI 辅助
本文研究一族介于超立方体与结合多面体之间的多面体，给出其正规扇的弦图描述，推广佩尔数并渐近于卡塔兰数，且所有多面体均产生二元几何。
中文摘要 AI 辅助
我们研究了一族在超立方体与结合多面体之间进行插值的多面体。我们给出了它们正规扇的显式描述，并通过与其顶点关联的弦图来描述其组合性质。这产生了推广佩尔数且渐近于卡塔兰数的有趣数列。我们以星形细分来描述正规扇之间的过渡，并将它们与Dyck路径相关的多面体（如[Veronica Calvo Cortes和Hadleigh Frost. Dyck路径、配置空间与线性Nakayama代数的多面体. https://arxiv.org/abs/2602.04571]）以及[Carolina Benedetti, Nantel Bergeron和John Machacek. 超图多面体：组合性质与反极. Journal of Combinatorics. 2019]中定义的超图多面体联系起来。此外，我们族中的所有多面体都产生二元几何。
英文摘要
We study a family of polytopes interpolating between the hypercube and the associahedron. We give an explicit description of their normal fans and describe their combinatorics in terms of chord diagrams associated to their vertices. This yields interesting number sequences generalizing Pell numbers and asymptotic to Catalan numbers. We describe the transition between the normal fans in terms of star subdivisions and relate them to polytopes associated to Dyck paths as in [Veronica Calvo Cortes and Hadleigh Frost. Dyck paths, Configuration Spaces and Polytopes for Linear Nakayama algebras. https://arxiv.org/abs/2602.04571] and hypergraphic polytopes defined in [Carolina Benedetti, Nantel Bergeron, and John Machacek. Hypergraphic polytopes: combinatorial properties and antipode. Journal of Combinatorics. 2019]. Furthermore, all polytopes in our families yield binary geometries.
发表机构
- Universidad Nacional Autónoma de México（墨西哥国立自治大学）
- University of Southampton（南安普顿大学）
机构由 AI 辅助整理，请以论文原文为准。
