Cyclic inclusion-exclusion and the kernel of P -partitions
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 d...
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Format: | Article |
Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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Series: | Discrete Mathematics & Theoretical Computer Science |
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Online Access: | https://dmtcs.episciences.org/6344/pdf |
Summary: | 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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ISSN: | 1365-8050 |