Dyck tilings, linear extensions, descents, and inversions
Dyck tilings were introduced by Kenyon and Wilson in their study of double-dimer pairings. They are certain kinds of tilings of skew Young diagrams with ribbon tiles shaped like Dyck paths. We give two bijections between "cover-inclusive'' Dyck tilings and linear extensions of tree po...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2012-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3081/pdf |
| _version_ | 1797270318711046144 |
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| author | Jang Soo Kim Karola Mészáros Greta Panova David B. Wilson |
| author_facet | Jang Soo Kim Karola Mészáros Greta Panova David B. Wilson |
| author_sort | Jang Soo Kim |
| collection | DOAJ |
| description | Dyck tilings were introduced by Kenyon and Wilson in their study of double-dimer pairings. They are certain kinds of tilings of skew Young diagrams with ribbon tiles shaped like Dyck paths. We give two bijections between "cover-inclusive'' Dyck tilings and linear extensions of tree posets. The first bijection maps the statistic (area + tiles)/2 to inversions of the linear extension, and the second bijection maps the "discrepancy'' between the upper and lower boundary of the tiling to descents of the linear extension. |
| first_indexed | 2024-04-25T02:02:22Z |
| format | Article |
| id | doaj.art-efd6baa900c643b39196bcdd5646a919 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:22Z |
| publishDate | 2012-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-efd6baa900c643b39196bcdd5646a9192024-03-07T14:51:45ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502012-01-01DMTCS Proceedings vol. AR,...Proceedings10.46298/dmtcs.30813081Dyck tilings, linear extensions, descents, and inversionsJang Soo Kim0Karola Mészáros1Greta Panova2David B. Wilson3University of Minnesota [Twin Cities]Department of Mathematics [Ann Arbor]University of California [Los Angeles]Microsoft Research [Redmond]Dyck tilings were introduced by Kenyon and Wilson in their study of double-dimer pairings. They are certain kinds of tilings of skew Young diagrams with ribbon tiles shaped like Dyck paths. We give two bijections between "cover-inclusive'' Dyck tilings and linear extensions of tree posets. The first bijection maps the statistic (area + tiles)/2 to inversions of the linear extension, and the second bijection maps the "discrepancy'' between the upper and lower boundary of the tiling to descents of the linear extension.https://dmtcs.episciences.org/3081/pdfdyck pathlinear extensiontree posetperfect matchingdyck tiling[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Jang Soo Kim Karola Mészáros Greta Panova David B. Wilson Dyck tilings, linear extensions, descents, and inversions Discrete Mathematics & Theoretical Computer Science dyck path linear extension tree poset perfect matching dyck tiling [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Dyck tilings, linear extensions, descents, and inversions |
| title_full | Dyck tilings, linear extensions, descents, and inversions |
| title_fullStr | Dyck tilings, linear extensions, descents, and inversions |
| title_full_unstemmed | Dyck tilings, linear extensions, descents, and inversions |
| title_short | Dyck tilings, linear extensions, descents, and inversions |
| title_sort | dyck tilings linear extensions descents and inversions |
| topic | dyck path linear extension tree poset perfect matching dyck tiling [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/3081/pdf |
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