Further developements in finite fibonomial calculus

TL;DR

This paper advances finite fibonomial operator calculus by presenting new definitions, combinatorial interpretations, and algebraic elements related to the Fibonacci cobweb poset, enriching the mathematical framework.

Contribution

It introduces novel definitions and observations in finite fibonomial calculus, including a combinatorial interpretation and algebraic elements of the Fibonacci cobweb poset.

Findings

New definitions and notation for finite fibonomial operator calculus.

A combinatorial interpretation of fibonomial coefficients using Fibonacci cobweb poset.

Elements of the incidence algebra of the Fibonacci cobweb poset are defined.

Abstract

Primary definitions, notation and general observations of finite fibonomial operator calculus (ffoc) are presented. Kwasniewski's combinatorial interpretation of fibonomial coefficients by the use of fibonacci cobweb poset is given. Some elements of incidence algebra of fibonacci cobweb poset are defined.