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.