Counting Shi regions with a fixed separating wall
Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant regions which have the fixed hyperplane as a sepa...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2011-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2916/pdf |
| _version_ | 1827324002848210944 |
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| author | Susanna Fishel Eleni Tzanaki Monica Vazirani |
| author_facet | Susanna Fishel Eleni Tzanaki Monica Vazirani |
| author_sort | Susanna Fishel |
| collection | DOAJ |
| description | Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant regions which have the fixed hyperplane as a separating wall; that is, regions where the hyperplane supports a facet of the region and separates the region from the origin. |
| first_indexed | 2024-04-25T02:02:52Z |
| format | Article |
| id | doaj.art-60d63f61d2af4fe8ab9620894f7e37f2 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:52Z |
| publishDate | 2011-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-60d63f61d2af4fe8ab9620894f7e37f22024-03-07T14:49:33ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502011-01-01DMTCS Proceedings vol. AO,...Proceedings10.46298/dmtcs.29162916Counting Shi regions with a fixed separating wallSusanna Fishel0Eleni Tzanaki1Monica Vazirani2School of Mathematical and Statistical Sciences (Arizona, Tempe)Department of Applied Mathematics [Heraklion]Department of Mathematics [Univ California Davis]Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant regions which have the fixed hyperplane as a separating wall; that is, regions where the hyperplane supports a facet of the region and separates the region from the origin.https://dmtcs.episciences.org/2916/pdfshi arrangementpartitions[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Susanna Fishel Eleni Tzanaki Monica Vazirani Counting Shi regions with a fixed separating wall Discrete Mathematics & Theoretical Computer Science shi arrangement partitions [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Counting Shi regions with a fixed separating wall |
| title_full | Counting Shi regions with a fixed separating wall |
| title_fullStr | Counting Shi regions with a fixed separating wall |
| title_full_unstemmed | Counting Shi regions with a fixed separating wall |
| title_short | Counting Shi regions with a fixed separating wall |
| title_sort | counting shi regions with a fixed separating wall |
| topic | shi arrangement partitions [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2916/pdf |
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