Formulae for Askey-Wilson moments and enumeration of staircase tableaux
We explain how the moments of the (weight function of the) Askey-Wilson polynomials are related to the enumeration of the staircase tableaux introduced by the first and fourth authors. This gives us a direct combinatorial formula for these moments, which is related to, but more elegant than the form...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
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American Mathematical Society (AMS)
2018
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| Online Access: | http://hdl.handle.net/1721.1/116192 https://orcid.org/0000-0003-3123-8241 |
| _version_ | 1811071768220139520 |
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| author | Corteel, S. Stanton, D. Williams, L. Stanley, Richard P |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Corteel, S. Stanton, D. Williams, L. Stanley, Richard P |
| author_sort | Corteel, S. |
| collection | MIT |
| description | We explain how the moments of the (weight function of the) Askey-Wilson polynomials are related to the enumeration of the staircase tableaux introduced by the first and fourth authors. This gives us a direct combinatorial formula for these moments, which is related to, but more elegant than the formula given in their earlier paper. Then we use techniques developed by Ismail and the third author to give explicit formulae for these moments and for the enumeration of staircase tableaux. Finally we study the enumeration of staircase tableaux at various specializations of the parameterizations; for example, we obtain the Catalan numbers, Fibonacci numbers, Eulerian numbers, the number of permutations, and the number of matchings. |
| first_indexed | 2024-09-23T08:55:55Z |
| format | Article |
| id | mit-1721.1/116192 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T08:55:55Z |
| publishDate | 2018 |
| publisher | American Mathematical Society (AMS) |
| record_format | dspace |
| spelling | mit-1721.1/1161922022-10-25T05:15:41Z Formulae for Askey-Wilson moments and enumeration of staircase tableaux Corteel, S. Stanton, D. Williams, L. Stanley, Richard P Massachusetts Institute of Technology. Department of Mathematics Stanley, Richard P We explain how the moments of the (weight function of the) Askey-Wilson polynomials are related to the enumeration of the staircase tableaux introduced by the first and fourth authors. This gives us a direct combinatorial formula for these moments, which is related to, but more elegant than the formula given in their earlier paper. Then we use techniques developed by Ismail and the third author to give explicit formulae for these moments and for the enumeration of staircase tableaux. Finally we study the enumeration of staircase tableaux at various specializations of the parameterizations; for example, we obtain the Catalan numbers, Fibonacci numbers, Eulerian numbers, the number of permutations, and the number of matchings. 2018-06-11T14:18:13Z 2018-06-11T14:18:13Z 2012-05 2010-08 2018-06-08T16:37:37Z Article http://purl.org/eprint/type/JournalArticle 0002-9947 1088-6850 http://hdl.handle.net/1721.1/116192 Corteel, S. et al. “Formulae for Askey-Wilson Moments and Enumeration of Staircase Tableaux.” Transactions of the American Mathematical Society 364, 11 (November 2012): 6009–6037 © 2012 American Mathematical Society https://orcid.org/0000-0003-3123-8241 http://dx.doi.org/10.1090/S0002-9947-2012-05588-7 Transactions of the American Mathematical Society 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. application/pdf American Mathematical Society (AMS) American Mathematical Society |
| spellingShingle | Corteel, S. Stanton, D. Williams, L. Stanley, Richard P Formulae for Askey-Wilson moments and enumeration of staircase tableaux |
| title | Formulae for Askey-Wilson moments and enumeration of staircase tableaux |
| title_full | Formulae for Askey-Wilson moments and enumeration of staircase tableaux |
| title_fullStr | Formulae for Askey-Wilson moments and enumeration of staircase tableaux |
| title_full_unstemmed | Formulae for Askey-Wilson moments and enumeration of staircase tableaux |
| title_short | Formulae for Askey-Wilson moments and enumeration of staircase tableaux |
| title_sort | formulae for askey wilson moments and enumeration of staircase tableaux |
| url | http://hdl.handle.net/1721.1/116192 https://orcid.org/0000-0003-3123-8241 |
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