Composite Linear Quotient Orderings of Ideals and Modified Anticycles

TL;DR

This paper introduces a new construction for linear quotient orderings of products of ideals with linear quotients and applies it to modified anticycle graphs, demonstrating their squares and cubes also have linear quotients.

Contribution

It presents a novel construction method for linear quotient orderings of ideal products and extends the class of graphs with linear quotients to their powers.

Findings

Constructed linear quotient orderings for products of ideals with linear quotients.

Applied the construction to modified anticycle graphs.

Showed that the square and cube of these graphs have linear quotients.

Abstract

In this paper we give a construction for a linear quotient ordering of a class of products of two ideals which have linear quotients. We apply this construction to give a class of modified anticycle graphs whose square and cube have linear quotients.