2009/10/02 by Burgunder, Emily, Ronco, Maria · 1 citation
#05E05 #17A30 #17A50 #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.0910.0403
We extend the definition of tridendriform bialgebra by introducing a weight q. The subspace of primitive elements of a q-tridendriform bialgebra is equipped with an associative product and a natural structure of brace algebra, related by a distributive law. This data is called q-Gerstenhaber-Voronov algebras. We prove the equivalence between the categories of connected q-tridendriform bialgebras and of q-Gerstenhaber-Voronov algebras. The space spanned by surjective maps, as well as the space spanned by parking functions, have natural structures of q-tridendriform bialgebras, denoted ST(q) and PQSym(q)*, in such a way that ST(q) is a sub-tridendriform bialgebra of PQSym(q)*. Finally we show that the bialgebra of M-permutations defined by T. Lam and P. Pylyavskyy may be endowed with a natural structure of q-tridendriform algebra which is a quotient of ST(q).