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 grap...
A lot of combinatorial objects have algebra and coalgebra structures and posets are important combinatorial objects. In this paper, we construct algebra and coalgebra structures on the vector space spanned by posets. ...