HOPF ALGEBRAS OF DIAGRAMS

Abstract

We investigate several generalizations of the Hopf algebra MQSym whose constructions come from labelings of special diagrams in bijection with packed matrices. Their products come either from the Hopf algebras WSym or WQSym, respectively built on integer set partitions and set compositions. Realizations on bi-word are exhibited, and it is shown how these algebras fit into a commutative diagram. Hopf deformations and dendriform structures are also considered for some algebras in the picture.