Depth of powers of the edge ideal of an increasing weighted path

TL;DR

This paper derives exact formulas for the depth of the quotient ring of powers of the edge ideal associated with an increasing weighted path, advancing algebraic understanding of such structures.

Contribution

It introduces precise formulas for the depth of powers of the edge ideal of increasing weighted paths, a novel contribution in algebraic combinatorics.

Findings

Exact formulas for the depth of the quotient ring of powers of the edge ideal.

Provides algebraic insights into weighted path structures.

Advances theoretical understanding of edge ideals in combinatorics.

Abstract

We provide exact formulas for the depth of the quotient ring of powers of the edge ideal of an increasing weighted path.