The Hopf Monoid of Hypergraphs and its Sub-Monoids: Basic Invariant and Reciprocity Theorem
The Hopf Monoid of Hypergraphs and its Sub-Monoids: Basic Invariant and Reciprocity Theorem
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超图的Hopf幺半群及其子幺半群：基本不变量和互易定理
DOI：
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发表时间：
2018
影响因子：
0.7
通讯作者：
A. Tanasa
中科院分区：
文献类型：
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作者：
J. Aval;T. Karaboghossian;A. Tanasa
在arXiv：1709.07504中，Aguiar和Ardila给出了超图上的一个Hopf幺半群结构以及Hopf幺半群上多项式不变量的一般构造。利用这些结果，本文定义了超图上一个新的多项式不变量。我们给出了负整数上这个不变量的组合解释，从而导出了超图上的互反定理。最后，我们使用这个不变量来恢复其他组合对象（图，单纯复形，建筑集等）以及相关的互易定理的著名不变量。
In arXiv:1709.07504 Aguiar and Ardila give a Hopf monoid structure on hypergraphs as well as a general construction of polynomial invariants on Hopf monoids. Using these results, we define in this paper a new polynomial invariant on hypergraphs. We give a combinatorial interpretation of this invariant on negative integers which leads to a reciprocity theorem on hypergraphs. Finally, we use this invariant to recover well-known invariants on other combinatorial objects (graphs, simplicial complexes, building sets, etc) as well as the associated reciprocity theorems.