论文标题
HOPF多项式不变的组合表达式
Combinatorial expressions of Hopf polynomial invariants
论文作者
论文摘要
在2017年，Aguiar和Ardila提供了一种通用方法，可以使用Hopf Monoid和Hopf Monoids的字符构建组合对象的多项式不变。他们表明，可以使用反座模式在负整数上找到对这些多项式的组合解释，并为广义固定图上的对抗物模具提供无取消的分组公式。在这项工作中，我们对这些多项式对正整数和负整数进行了组合解释，用于广泛的Persutahedra和HyperGraphs的Hopf Monoid，以及这两个Hopf Monoids上的每个角色。在超图的情况下，我们为负整数的解释提供了两种不同的证据。然后，我们在其他组合对象上推断出相似的结果，包括图形，简单络合物和建筑集。
In 2017 Aguiar and Ardila provided a generic way to construct polynomial invariants of combinatorial objects using the notions of Hopf monoids and characters of Hopf monoids. They show that it is possible to find a combinatorial interpretation of these polynomials over negative integers using the antipode and give a cancellation-free grouping-free formula for the antipode on generalized permutahedra. In this work, we give a combinatorial interpretation of these polynomials over both positive integers and negative integers for the Hopf monoids of generalized permutahedra and hypergraphs and for every character on these two Hopf monoids. In the case of hypergraphs, we present two different proofs for the interpretation on negative integers. We then deduce similar results on other combinatorial objects including graphs, simplicial complexes and building sets.
