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.
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