Journal article
Lecture hall graphs and the Askey scheme
- Abstract:
- We establish, for every family of orthogonal polynomials in the q-Askey scheme and the Askey scheme, a combinatorial model for mixed moments and coefficients in terms of paths on the lecture hall graph. This generalizes the previous results of Corteel and Kim for the little q-Jacobi polynomials. We build these combinatorial models by bootstrapping, beginning with polynomials at the bottom and working towards Askey-Wilson polynomials which sit at the top of the q-Askey scheme. As an application of the theory, we provide the first combinatorial proof of the symmetries in the parameters of the Askey–Wilson polynomials.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
-
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(Preview, Accepted manuscript, pdf, 549.3KB, Terms of use)
-
- Publisher copy:
- 10.1016/j.aim.2026.111056
Authors
+ U.S. National Science Foundation
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- Funder identifier:
- https://ror.org/021nxhr62
- Grant:
- DMS-2054482
+ National Research Foundation of Korea
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- Funder identifier:
- https://ror.org/013aysd81
- Grant:
- RS-2025-00557835
+ European Research Council
More from this funder
- Funder identifier:
- https://ror.org/0472cxd90
- Grant:
- 740900
+ Agence Nationale de la Recherche
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- Funder identifier:
- https://ror.org/00rbzpz17
- Grant:
- ANR-18-CE40-0033
- ANR-19-CE48-0011
- Publisher:
- Elsevier
- Journal:
- Advances in Mathematics More from this journal
- Volume:
- 499
- Article number:
- 111056
- Publication date:
- 2026-05-26
- Acceptance date:
- 2026-05-14
- DOI:
- EISSN:
-
1090-2082
- ISSN:
-
0001-8708
- Language:
-
English
- Keywords:
- Pubs id:
-
2426152
- Local pid:
-
pubs:2426152
- Source identifiers:
-
W4388964318
- Deposit date:
-
2026-05-28
- ARK identifier:
Terms of use
- Copyright holder:
- Elsevier Inc.
- Copyright date:
- 2026
- Rights statement:
- ©2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
- Notes:
- The author accepted manuscript (AAM) of this paper has been made available under the University of Oxford's Open Access Publications Policy, and a CC BY public copyright licence has been applied.
- Licence:
- CC Attribution (CC BY)
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