Comments on combinatorial interpretation of fibonomial coefficients - an email style letter

TL;DR

This paper discusses a recent combinatorial interpretation of Fibonomial coefficients, filling a 126-year gap since their initial definition, and highlights the historical context and recent developments.

Contribution

It presents a new combinatorial interpretation of Fibonomial coefficients, extending the understanding of these coefficients in the context of classical combinatorics.

Findings

A join combinatorial interpretation for Fibonomial coefficients has been established.

This interpretation applies to all binomial-type coefficients, including Fibonomial coefficients.

The work bridges historical gaps in the understanding of Fibonomial coefficients.

Abstract

Up to our knowledge -since about 126 years we were lacking of classical type combinatorial interpretation of Fibonomial coefficients as it was Lukas \cite{1} - to our knowledge -who was the first who had defined Finonomial coefficients and derived a recurrence for them (see Historical Note in \cite{2,3}). Here we inform that a join combinatorial interpretation was found \cite{4} for all binomial-type coefficient - Fibonomial coefficients included.