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

Jiaming Dong; Huilan Li; Jiaming Dong; Huilan Li

doi:10.3934/mmc.2024004

Mathematical Modelling and Control

2024, Volume 4, Issue 1: 32-43. doi: 10.3934/mmc.2024004

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Research article

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

Jiaming Dong ,
Huilan Li ^,

School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China

Received: 18 January 2023 Revised: 21 March 2023 Accepted: 08 April 2023 Published: 19 March 2024

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.
- Hopf algebra,
- labeled simple graph,
- super-shuffle product,
- cut-box coproduct
Citation: Jiaming Dong, Huilan Li. Hopf algebra of labeled simple graphs arising from super-shuffle product[J]. Mathematical Modelling and Control, 2024, 4(1): 32-43. doi: 10.3934/mmc.2024004

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Abstract

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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