%0 Journal Article
%T Super-Shuffle Product and Cut-Box Coproduct on (0,1)-Matrices
%A Sifan Song
%A Huilan Li
%J Open Journal of Applied Sciences
%P 1326-1335
%@ 2165-3925
%D 2023
%I Scientific Research Publishing
%R 10.4236/ojapps.2023.138105
%X 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.
%K (0
%K 1)-Matrix
%K Super-Shuffle Product
%K Cut-Box Coproduct
%K Graded Algebra
%K Graded Coalgebra
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=127114