Graded posets inverse zeta matrix formula

TL;DR

This paper derives an explicit formula for the inverse zeta matrix of graded posets with finitely many minimal elements, providing combinatorial interpretations and introducing special number theoretic code triangles.

Contribution

It presents a new explicit formula for the inverse zeta matrix of graded posets and offers novel combinatorial interpretations involving number theoretic code triangles.

Findings

Explicit inverse zeta matrix formula for graded posets.

Introduction of special number theoretic code triangles.

Combinatorial interpretation of F-nomial coefficients.

Abstract

We derive the explicit formula for the inverse of zeta matrix for any graded posets with the finite set of minimal elements . The combinatorial interpretation of this result is given. For that to do special number theoretic code triangles for graded posets are proposed and apart from the present author combinatorial interpretation of $F-nomial$ coefficients another one is proposed referring to the number of all maximal chains in the corresponding poset intervals.