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 tableaux. In thi...
Published in: | Communications in Mathematical Physics |
---|---|
Main Authors: | , , |
Other Authors: | |
Format: | Article in Journal/Newspaper |
Language: | English |
Published: |
Springer Berlin Heidelberg
2021
|
Subjects: | |
Online Access: | https://hdl.handle.net/1721.1/132061 |
id |
ftmit:oai:dspace.mit.edu:1721.1/132061 |
---|---|
record_format |
openpolar |
spelling |
ftmit:oai:dspace.mit.edu:1721.1/132061 2023-10-09T21:48:23+02:00 Arctic Curves Phenomena for Bounded Lecture Hall Tableaux Corteel, Sylvie Keating, David Nicoletti, Matthew Massachusetts Institute of Technology. Department of Mathematics 2021-03-18T04:35:30Z application/pdf https://hdl.handle.net/1721.1/132061 en eng Springer Berlin Heidelberg https://doi.org/10.1007/s00220-021-03952-z https://hdl.handle.net/1721.1/132061 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 Springer Berlin Heidelberg Article http://purl.org/eprint/type/JournalArticle 2021 ftmit https://doi.org/10.1007/s00220-021-03952-z 2023-09-18T18:04:24Z 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. Article in Journal/Newspaper Arctic DSpace@MIT (Massachusetts Institute of Technology) Arctic Communications in Mathematical Physics 382 3 1449 1493 |
institution |
Open Polar |
collection |
DSpace@MIT (Massachusetts Institute of Technology) |
op_collection_id |
ftmit |
language |
English |
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. |
author2 |
Massachusetts Institute of Technology. Department of Mathematics |
format |
Article in Journal/Newspaper |
author |
Corteel, Sylvie Keating, David Nicoletti, Matthew |
spellingShingle |
Corteel, Sylvie Keating, David Nicoletti, Matthew Arctic Curves Phenomena for Bounded Lecture Hall Tableaux |
author_facet |
Corteel, Sylvie Keating, David Nicoletti, Matthew |
author_sort |
Corteel, Sylvie |
title |
Arctic Curves Phenomena for Bounded Lecture Hall Tableaux |
title_short |
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_sort |
arctic curves phenomena for bounded lecture hall tableaux |
publisher |
Springer Berlin Heidelberg |
publishDate |
2021 |
url |
https://hdl.handle.net/1721.1/132061 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
Springer Berlin Heidelberg |
op_relation |
https://doi.org/10.1007/s00220-021-03952-z https://hdl.handle.net/1721.1/132061 |
op_rights |
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 |
op_doi |
https://doi.org/10.1007/s00220-021-03952-z |
container_title |
Communications in Mathematical Physics |
container_volume |
382 |
container_issue |
3 |
container_start_page |
1449 |
op_container_end_page |
1493 |
_version_ |
1779311474792988672 |