Super quasi-symmetric functions via Young diagrams

Abstract

We consider the multivariate generating series $F_P$ of $P$-partitions in infinitely many variables $x_1,x_2,\dots$. For some family of ranked posets $P$, it is natural to consider an analog $N_P$ with two infinite alphabets. When we collapse these two alphabets, we trivially recover $F_P$. Our main result is the converse, that is, the explicit construction of a map sending back $F_P$ onto $N_P$. We also give a noncommutative analog of the latter. An application is the construction of a basis of WQSym with a non-negative multiplication table, which lifts a basis of QSym introduced by K. Luoto.

12 pages, extended abstract of arXiv:1312.2727, presented at FPSAC conference. The presentation of the results is quite different from the long version