Following the lead of Stanley and Gessel, we consider a linear map which associates to an acyclic directed graph (or a poset) a quasi-symmetric function. The latter is naturally defined as multivariate generating series of non-decreasing functions on the graph (or of P -partitions of the poset).We describe the kernel of this linear map, using a simple combinatorial operation that we call cyclic inclusion- exclusion. Our result also holds for the natural non-commutative analog and for the commutative and non-commutative restrictions to bipartite graphs.

Source : oai:HAL:hal-02173373v1

Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)

Published on: April 22, 2020

Submitted on: July 4, 2016

Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

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