On Characteristic Polynomials of the Family of Cobweb Posets

Abstract

This note is a response to one of problems posed by A.K. Kwasniewski in one of his recent papers. Namely for the sequence of finite cobweb subposets, the looked for explicit formulas for corresponding sequence of characteristic polynomials are discovered and delivered here. The recurrence relation defining arbitrary family of charactristic polynomials of finite cobweb posets is also derived.