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Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2020

Cyclic inclusion-exclusion and the kernel of P -partitions

Valentin Féray

Résumé

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.
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Dates et versions

hal-02173373 , version 1 (04-07-2019)

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Valentin Féray. Cyclic inclusion-exclusion and the kernel of P -partitions. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6344⟩. ⟨hal-02173373⟩
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