Hopf algebra of labeled simple graphs arising from super-shuffle product

From the connections between permutations and labeled simple graphs, we generalized the super-shuffle product and the cut-box coproduct on permutations to labeled simple graphs. We then proved that the vector space spanned by labeled simple graphs is a Hopf algebra with these two operations.

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Bibliographic Details
Published inMathematical modelling and control Vol. 4; no. 1; pp. 32 - 43
Main Authors Dong, Jiaming, Li, Huilan
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
cut-box coproduct
hopf algebra
labeled simple graph
super-shuffle product
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Summary:From the connections between permutations and labeled simple graphs, we generalized the super-shuffle product and the cut-box coproduct on permutations to labeled simple graphs. We then proved that the vector space spanned by labeled simple graphs is a Hopf algebra with these two operations.
ISSN:2767-8946
2767-8946
DOI:10.3934/mmc.2024004