2015/04/23 by Foissy, Loïc
#16T05 #16W10 #18D50 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1504.06056
We study quadri-algebras and dual quadri-algebras. We describe the free quadri-algebra on one generator as a subobject of the Hopf algebra of permutations FQSym, proving a conjecture due to Aguiar and Loday, using that the operad of quadri-algebras can be obtained from the operad of dendriform algebras by both black and white Manin products. We also give a combinatorial description of free dual quadri-algebras. A notion of quadri-bialgebra is also introduced, with applications to the Hopf algebras FQSym and WQSym.