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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 076, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.076 (Mi sigma1613) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Elliptic and $q$-Analogs of the Fibonomial Numbers

Nantel Bergerona, Cesar Ceballosb, Josef Küstnerc

a Department of Mathematics and Statistics, York University, Toronto, Canada
b Institute of Geometry, TU Graz, Graz, Austria
c Faculty of Mathematics, University of Vienna, Vienna, Austria
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DOI: https://doi.org/10.3842/SIGMA.2020.076
Abstract: 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 $q$-analog and elliptic analog of the Fibonomial numbers. This is achieved by introducing some $q$-weights and elliptic weights to a slight modification of the combinatorial model of Sagan and Savage.
Keywords: Fibonomial, Fibonacci, $q$-analog, elliptic analog, weighted enumeration.
Funding agency Grant number
Natural Sciences and Engineering Research Council of Canada (NSERC)
Austrian Science Fund F 5008-N15
P 32305
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.
Received: March 14, 2020; in final form July 29, 2020; Published online August 13, 2020
Bibliographic databases:
Document Type: Article
MSC: 11B39, 05A30, 05A10
Language: English
Citation: Nantel Bergeron, Cesar Ceballos, Josef Küstner, “Elliptic and $q$-Analogs of the Fibonomial Numbers”, SIGMA, 16 (2020), 076, 16 pp.
Citation in format AMSBIB
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\paper Elliptic and $q$-Analogs of the Fibonomial Numbers
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\vol 16
\papernumber 076
\totalpages 16
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    • This publication is cited in the following 1 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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