Negative moments of orthogonal polynomials
If a sequence indexed by nonnegative integers satisfies a linear recurrence without constant terms, one can extend the indices of the sequence to negative integers using the recurrence. Recently, Cigler and Krattenthaler showed that the negative version of the number of bounded Dyck paths is the num...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2023-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509423000233/type/journal_article |
| _version_ | 1797857755830157312 |
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| author | Jihyeug Jang Donghyun Kim Jang Soo Kim Minho Song U-Keun Song |
| author_facet | Jihyeug Jang Donghyun Kim Jang Soo Kim Minho Song U-Keun Song |
| author_sort | Jihyeug Jang |
| collection | DOAJ |
| description | If a sequence indexed by nonnegative integers satisfies a linear recurrence without constant terms, one can extend the indices of the sequence to negative integers using the recurrence. Recently, Cigler and Krattenthaler showed that the negative version of the number of bounded Dyck paths is the number of bounded alternating sequences. In this paper, we provide two methods to compute the negative versions of sequences related to moments of orthogonal polynomials. We give a combinatorial model for the negative version of the number of bounded Motzkin paths. We also prove two conjectures of Cigler and Krattenthaler on reciprocity between determinants. |
| first_indexed | 2024-04-09T21:01:55Z |
| format | Article |
| id | doaj.art-8520bbb51855413b97e51bfd07134059 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-09T21:01:55Z |
| publishDate | 2023-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-8520bbb51855413b97e51bfd071340592023-03-29T08:38:30ZengCambridge University PressForum of Mathematics, Sigma2050-50942023-01-011110.1017/fms.2023.23Negative moments of orthogonal polynomialsJihyeug Jang0Donghyun Kim1Jang Soo Kim2Minho Song3U-Keun Song4Department of Mathematics, Sungkyunkwan University, Suwon, South Korea; E-mail:Applied Algebra and Optimization Research Center, Sungkyunkwan University, Suwon, South Korea; E-mail:Department of Mathematics, Sungkyunkwan University, Suwon, South Korea; E-mail:Applied Algebra and Optimization Research Center, Sungkyunkwan University, Suwon, South Korea; E-mail:Department of Mathematics, Sungkyunkwan University, Suwon, South Korea; E-mail:If a sequence indexed by nonnegative integers satisfies a linear recurrence without constant terms, one can extend the indices of the sequence to negative integers using the recurrence. Recently, Cigler and Krattenthaler showed that the negative version of the number of bounded Dyck paths is the number of bounded alternating sequences. In this paper, we provide two methods to compute the negative versions of sequences related to moments of orthogonal polynomials. We give a combinatorial model for the negative version of the number of bounded Motzkin paths. We also prove two conjectures of Cigler and Krattenthaler on reciprocity between determinants.https://www.cambridge.org/core/product/identifier/S2050509423000233/type/journal_article05A1505A19 |
| spellingShingle | Jihyeug Jang Donghyun Kim Jang Soo Kim Minho Song U-Keun Song Negative moments of orthogonal polynomials Forum of Mathematics, Sigma 05A15 05A19 |
| title | Negative moments of orthogonal polynomials |
| title_full | Negative moments of orthogonal polynomials |
| title_fullStr | Negative moments of orthogonal polynomials |
| title_full_unstemmed | Negative moments of orthogonal polynomials |
| title_short | Negative moments of orthogonal polynomials |
| title_sort | negative moments of orthogonal polynomials |
| topic | 05A15 05A19 |
| url | https://www.cambridge.org/core/product/identifier/S2050509423000233/type/journal_article |
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