Elliptic and $q$-Analogs of the Fibonomial Numbers

Symmetry Integrability and Geometry-Methods and Applications

article

Nantel Bergeron¹  Cesar Ceballos²  Josef Küstner³ 

[1] Department of Mathematics and Statistics, York University;Institute of Geometry;Faculty of Mathematics, University of Vienna

关键词: Fibonomial;    Fibonacci;    q-analog;    elliptic analog;    weighted enumeration;   

DOI  :  10.3842/SIGMA.2020.076

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown