从图行走中的时序循环擦除看共同预列结构

IF 1 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics Pub Date : 2024-04-12 DOI:10.1016/j.ejc.2024.103967

Loïc Foissy , Pierre-Louis Giscard , Cécile Mammez

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引用次数: 0

摘要

我们证明，按时间顺序删除图上走行的循环（即劳勒的循环删除程序），会在走行所跨的向量空间上生成一个前李共生代数。此外，我们还证明了图漫步的张量代数和对称代数是霍普夫代数，明确提供了它们的反节点，并从图漫步的张量代数上的括号联合代数恢复了前李共代数。最后，我们展示了与特定类型的图走相关的子霍普夫代数。

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A co-preLie structure from chronological loop erasure in graph walks

We show that the chronological removal of cycles from a walk on a graph, known as Lawler’s loop-erasing procedure, generates a preLie co-algebra on the vector space spanned by the walks. In addition, we prove that the tensor and symmetric algebras of graph walks are Hopf algebras, provide their antipodes explicitly and recover the preLie co-algebra from a brace coalgebra on the tensor algebra of graph walks. Finally we exhibit sub-Hopf algebras associated to particular types of walks.

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来源期刊

European Journal of Combinatorics 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.