Trees whose path ideals have linear quotients

TL;DR

This paper classifies all trees whose path ideals of any length n possess the algebraic property of linear quotients, advancing understanding of the algebraic structure of tree-based ideals.

Contribution

It provides a complete classification of trees with n-path ideals that have linear quotients, a novel result in algebraic combinatorics.

Findings

Identifies specific tree structures with linear quotient properties.

Establishes criteria for n-path ideals to have linear quotients.

Completes classification for all trees and path lengths n.

Abstract

For any integer $n$, we classify all trees whose $n$-path ideals have linear quotients.