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Liu, M. and Li, H. (2021) A Hopf Algebra on Permutations Arising from Super-Shuffle Product. Symmetry, 13, Article No. 1010.
https://doi.org/10.3390/sym13061010

has been cited by the following article:

• TITLE: Super-Shuffle Product and Cut-Box Coproduct on (0,1)-Matrices

  AUTHORS: Sifan Song, Huilan Li

  KEYWORDS: (0, 1)-Matrix, Super-Shuffle Product, Cut-Box Coproduct, Graded Algebra, Graded Coalgebra

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.13 No.8, August 22, 2023

  ABSTRACT: In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.