On the ranks of configurations on the complete graph
We consider the parameter rank introduced for graph configurations by M. Baker and S. Norine. We focus on complete graphs and obtain an efficient algorithm to determine the rank for these graphs. The analysis of this algorithm leads to the definition of a parameter on Dyck words, which we call prera...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2013-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2332/pdf |
| _version_ | 1827323987575701504 |
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| author | Robert Cori Yvan Le Borgne |
| author_facet | Robert Cori Yvan Le Borgne |
| author_sort | Robert Cori |
| collection | DOAJ |
| description | We consider the parameter rank introduced for graph configurations by M. Baker and S. Norine. We focus on complete graphs and obtain an efficient algorithm to determine the rank for these graphs. The analysis of this algorithm leads to the definition of a parameter on Dyck words, which we call prerank. We prove that the distribution of area and prerank on Dyck words of given length $2n$ leads to a polynomial with variables $q,t$ which is symmetric in these variables. This polynomial is different from the $q,t-$Catalan polynomial studied by A. Garsia, J. Haglund and M. Haiman. |
| first_indexed | 2024-04-25T02:01:30Z |
| format | Article |
| id | doaj.art-26f63d4bb4b240038ff0575a9083a6ed |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:01:30Z |
| publishDate | 2013-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-26f63d4bb4b240038ff0575a9083a6ed2024-03-07T14:52:36ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502013-01-01DMTCS Proceedings vol. AS,...Proceedings10.46298/dmtcs.23322332On the ranks of configurations on the complete graphRobert Cori0Yvan Le Borgne1Laboratoire Bordelais de Recherche en InformatiqueLaboratoire Bordelais de Recherche en InformatiqueWe consider the parameter rank introduced for graph configurations by M. Baker and S. Norine. We focus on complete graphs and obtain an efficient algorithm to determine the rank for these graphs. The analysis of this algorithm leads to the definition of a parameter on Dyck words, which we call prerank. We prove that the distribution of area and prerank on Dyck words of given length $2n$ leads to a polynomial with variables $q,t$ which is symmetric in these variables. This polynomial is different from the $q,t-$Catalan polynomial studied by A. Garsia, J. Haglund and M. Haiman.https://dmtcs.episciences.org/2332/pdfrankriemann-roch for graphscomplete graphsdyck words[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Robert Cori Yvan Le Borgne On the ranks of configurations on the complete graph Discrete Mathematics & Theoretical Computer Science rank riemann-roch for graphs complete graphs dyck words [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | On the ranks of configurations on the complete graph |
| title_full | On the ranks of configurations on the complete graph |
| title_fullStr | On the ranks of configurations on the complete graph |
| title_full_unstemmed | On the ranks of configurations on the complete graph |
| title_short | On the ranks of configurations on the complete graph |
| title_sort | on the ranks of configurations on the complete graph |
| topic | rank riemann-roch for graphs complete graphs dyck words [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2332/pdf |
| work_keys_str_mv | AT robertcori ontheranksofconfigurationsonthecompletegraph AT yvanleborgne ontheranksofconfigurationsonthecompletegraph |