Author(s)

Sifan Song, Huilan Li^*

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

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.

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

Song, S. and Li, H. (2023) Super-Shuffle Product and Cut-Box Coproduct on (0,1)-Matrices. Open Journal of Applied Sciences, 13, 1326-1335. doi: 10.4236/ojapps.2023.138105.