Basis of totally primitive elements of WQSym

03.12.2019 15:15 - 16:45

Hugo Mlodecki (Univ. Paris Sud)


By Foissy's work, the bidendriform structure of the Word Quasisymmetric Functions Hopf algebra (WQSym) implies that it is isomorphic to its dual and that it is entirely determined by so-called totally primitive elements (elements such that the two half-coproducts are 0). I will construct a basis indexed by a new combinatorial family called biplane forests in bijection with packed words.  In this basis, primitive elements are generated by biplane trees and totally primitive elements by a certain subset of trees.

Thus we obtain the first explicit basis for totally primitive elements of WQSym.


M. Drmota


TU Wien, Dissertantenraum, Freihaus, Turm A, 8. OG., Wiedner Hauptstr. 8-10, 1040 Wien