Mathematical Modelling and Control (Mar 2024)

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

  • Jiaming Dong ,
  • Huilan Li

DOI
https://doi.org/10.3934/mmc.2024004
Journal volume & issue
Vol. 4, no. 1
pp. 32 – 43

Abstract

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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.

Keywords