Elliptic and 𝑞-Analogs of the Fibonomial Numbers

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.