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 |
| _version_ | 1797270215900266496 |
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| author | Valentin Féray |
| author_facet | Valentin Féray |
| author_sort | Valentin Féray |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:00:44Z |
| format | Article |
| id | doaj.art-8d7f69b9345b41b1a84efd09f6deac38 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:44Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-8d7f69b9345b41b1a84efd09f6deac382024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.63446344Cyclic inclusion-exclusion and the kernel of P -partitionsValentin Féray0Institut für Mathematik [Zürich]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.https://dmtcs.episciences.org/6344/pdf[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Valentin Féray Cyclic inclusion-exclusion and the kernel of P -partitions Discrete Mathematics & Theoretical Computer Science [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | Cyclic inclusion-exclusion and the kernel of P -partitions |
| title_full | Cyclic inclusion-exclusion and the kernel of P -partitions |
| title_fullStr | Cyclic inclusion-exclusion and the kernel of P -partitions |
| title_full_unstemmed | Cyclic inclusion-exclusion and the kernel of P -partitions |
| title_short | Cyclic inclusion-exclusion and the kernel of P -partitions |
| title_sort | cyclic inclusion exclusion and the kernel of p partitions |
| topic | [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6344/pdf |
| work_keys_str_mv | AT valentinferay cyclicinclusionexclusionandthekernelofppartitions |