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arXiv · 1410.1772

Cyclic inclusion-exclusion

Valentin Féray
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Abstract

Following the lead of Stanley and Gessel, we consider a morphism 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. We describe the kernel of this morphism, using a simple combinatorial operation that we call cyclic inclusion-exclusion. Our result also holds for the natural noncommutative analog and for the commutative and noncommutative restrictions to bipartite graphs. An application to the theory of Kerov character polynomials is given.

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Valentin Féray. 2014-10-07. Cyclic inclusion-exclusion. https://arxiv.org/abs/1410.1772

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