Elliptic and $q$-Analogs of the Fibonomial Numbers

TL;DR

This paper develops combinatorial models for the $q$-analog and elliptic analog of Fibonomial numbers, extending previous work by incorporating $q$-weights and elliptic weights into the Fibonomial framework.

Contribution

It introduces new combinatorial descriptions for the $q$-analog and elliptic analog of Fibonomial numbers using weighted models.

Findings

Provides combinatorial models with $q$-weights

Extends to elliptic weights

Generalizes Fibonomial number representations

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.