Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 076, 16 pages      arXiv:1911.12785      https://doi.org/10.3842/SIGMA.2020.076
Contribution to the Special Issue on Elliptic Integrable Systems, Special Functions and Quantum Field Theory

Elliptic and $q$-Analogs of the Fibonomial Numbers

Nantel Bergeron a, Cesar Ceballos b and Josef Küstner c
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

Received March 14, 2020, in final form July 29, 2020; Published online August 13, 2020

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.

Key words: Fibonomial; Fibonacci; $q$-analog; elliptic analog; weighted enumeration.

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