Elliptic and -Analogs of the Fibonomial Numbers
In 2009, Sagan and Savage introduced a combinatorial model for the Fibonomial numbers, integer numbers that are obtained from the binomial coefficients by replacing each term by its corresponding Fibonacci number. In this paper, we present a combinatorial description for the -analog and elliptic ana...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210772 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Elliptic and -Analogs of the Fibonomial Numbers. Nantel Bergeron, Cesar Ceballos and Josef Küstner. SIGMA 16 (2020), 076, 16 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862666026633658368 |
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| author | Bergeron, Nantel Ceballos, Cesar Küstner, Josef |
| author_facet | Bergeron, Nantel Ceballos, Cesar Küstner, Josef |
| citation_txt | Elliptic and -Analogs of the Fibonomial Numbers. Nantel Bergeron, Cesar Ceballos and Josef Küstner. SIGMA 16 (2020), 076, 16 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In 2009, Sagan and Savage introduced a combinatorial model for the Fibonomial numbers, integer numbers that are obtained from the binomial coefficients by replacing each term by its corresponding Fibonacci number. In this paper, we present a combinatorial description for the -analog and elliptic analog of the Fibonomial numbers. This is achieved by introducing some -weights and elliptic weights to a slight modification of the combinatorial model of Sagan and Savage.
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| first_indexed | 2026-03-16T09:09:44Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210772 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T09:09:44Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bergeron, Nantel Ceballos, Cesar Küstner, Josef 2025-12-17T14:32:21Z 2020 Elliptic and -Analogs of the Fibonomial Numbers. Nantel Bergeron, Cesar Ceballos and Josef Küstner. SIGMA 16 (2020), 076, 16 pages 1815-0659 2020 Mathematics Subject Classification: 11B39; 05A30; 05A10 arXiv:1911.12785 https://nasplib.isofts.kiev.ua/handle/123456789/210772 https://doi.org/10.3842/SIGMA.2020.076 In 2009, Sagan and Savage introduced a combinatorial model for the Fibonomial numbers, integer numbers that are obtained from the binomial coefficients by replacing each term by its corresponding Fibonacci number. In this paper, we present a combinatorial description for the -analog and elliptic analog of the Fibonomial numbers. This is achieved by introducing some -weights and elliptic weights to a slight modification of the combinatorial model of Sagan and Savage. The authors are grateful to Farid Aliniaeifard, Tom Denton, Shu Xiao Li, Drew Armstrong, Bruce Sagan, Michael Schlosser, and Mike Zabrocki for helpful and inspiring discussions. We also thank anonymous referees for their useful comments and suggestions. NB was supported by NSERC and a York Research Chair. CC was supported by the Austrian Science Foundation FWF, grant F 5008-N15, in the framework of the Special Research Program Algorithmic and Enumerative Combinatorics. JK was supported by the Austrian Science Foundation FWF, grant P 32305. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Elliptic and -Analogs of the Fibonomial Numbers Article published earlier |
| spellingShingle | Elliptic and -Analogs of the Fibonomial Numbers Bergeron, Nantel Ceballos, Cesar Küstner, Josef |
| title | Elliptic and -Analogs of the Fibonomial Numbers |
| title_full | Elliptic and -Analogs of the Fibonomial Numbers |
| title_fullStr | Elliptic and -Analogs of the Fibonomial Numbers |
| title_full_unstemmed | Elliptic and -Analogs of the Fibonomial Numbers |
| title_short | Elliptic and -Analogs of the Fibonomial Numbers |
| title_sort | elliptic and -analogs of the fibonomial numbers |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210772 |
| work_keys_str_mv | AT bergeronnantel ellipticandanalogsofthefibonomialnumbers AT ceballoscesar ellipticandanalogsofthefibonomialnumbers AT kustnerjosef ellipticandanalogsofthefibonomialnumbers |