The First Ascent into the Incidence Algebra of the Fibonacci Cobweb Poset

TL;DR

This paper provides explicit formulas for the Möbius function and other key elements of the incidence algebra of the Fibonacci cobweb poset, utilizing Kwaśniewski's construction in the plane grid coordinate system.

Contribution

It introduces explicit formulas for the incidence algebra elements of the Fibonacci cobweb poset, advancing combinatorial and algebraic understanding of this structure.

Findings

Explicit formulas for the Möbius function are derived.

Key elements of the incidence algebra are characterized.

The construction is based on Kwaśniewski's approach in the plane grid coordinate system.

Abstract

The explicite formulas for m\"{o}biusien function and some other important elements of the incidence algebra are delivered. For that to do one uses kwa\'sniewski's construction of his fibonacci cobweb poset in the plane grid coordinate system.