Arctic Curves Phenomena for Bounded Lecture Hall Tableaux
Abstract Recently the first author and Jang Soo Kim introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. They then enumerated bounded lecture hall tableaux and showed that their enumeration is closely related to standard and semistandard Young t...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/132061 |
| _version_ | 1811079583150112768 |
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| author | Corteel, Sylvie Keating, David Nicoletti, Matthew |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Corteel, Sylvie Keating, David Nicoletti, Matthew |
| author_sort | Corteel, Sylvie |
| collection | MIT |
| description | Abstract
Recently the first author and Jang Soo Kim introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. They then enumerated bounded lecture hall tableaux and showed that their enumeration is closely related to standard and semistandard Young tableaux. In this paper we study the asymptotic behavior of these bounded tableaux thanks to two other combinatorial models: non-intersecting paths on a graph whose faces are squares and pentagons and dimer models on a lattice whose faces are hexagons and octagons. We use the tangent method to investigate the arctic curve in the model of non-intersecting lattice paths with fixed starting points and ending points distributed according to some arbitrary piecewise differentiable function. We then study the dimer model and use an ansatz to guess the asymptotics of the inverse of the Kasteleyn, which confirm the arctic curve computed with the tangent method for two examples. |
| first_indexed | 2024-09-23T11:17:19Z |
| format | Article |
| id | mit-1721.1/132061 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:17:19Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1320612023-09-15T18:38:00Z Arctic Curves Phenomena for Bounded Lecture Hall Tableaux Corteel, Sylvie Keating, David Nicoletti, Matthew Massachusetts Institute of Technology. Department of Mathematics Abstract Recently the first author and Jang Soo Kim introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. They then enumerated bounded lecture hall tableaux and showed that their enumeration is closely related to standard and semistandard Young tableaux. In this paper we study the asymptotic behavior of these bounded tableaux thanks to two other combinatorial models: non-intersecting paths on a graph whose faces are squares and pentagons and dimer models on a lattice whose faces are hexagons and octagons. We use the tangent method to investigate the arctic curve in the model of non-intersecting lattice paths with fixed starting points and ending points distributed according to some arbitrary piecewise differentiable function. We then study the dimer model and use an ansatz to guess the asymptotics of the inverse of the Kasteleyn, which confirm the arctic curve computed with the tangent method for two examples. 2021-09-20T17:41:44Z 2021-09-20T17:41:44Z 2021-03-10 2021-03-18T04:35:30Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/132061 en https://doi.org/10.1007/s00220-021-03952-z Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Corteel, Sylvie Keating, David Nicoletti, Matthew Arctic Curves Phenomena for Bounded Lecture Hall Tableaux |
| title | Arctic Curves Phenomena for Bounded Lecture Hall Tableaux |
| title_full | Arctic Curves Phenomena for Bounded Lecture Hall Tableaux |
| title_fullStr | Arctic Curves Phenomena for Bounded Lecture Hall Tableaux |
| title_full_unstemmed | Arctic Curves Phenomena for Bounded Lecture Hall Tableaux |
| title_short | Arctic Curves Phenomena for Bounded Lecture Hall Tableaux |
| title_sort | arctic curves phenomena for bounded lecture hall tableaux |
| url | https://hdl.handle.net/1721.1/132061 |
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