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arXiv · 1407.6258

Super quasi-symmetric functions via Young diagrams

Jean-Christophe Aval·Valentin Féray·Jean-Christophe Novelli·Jean-Yves Thibon
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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.

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Jean-Christophe Aval, Valentin Féray, Jean-Christophe Novelli, Jean-Yves Thibon. 2014-07-23. Super quasi-symmetric functions via Young diagrams. https://arxiv.org/abs/1407.6258

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