Some algebraic invariants of the residue class rings of the edge ideals of perfect semiregular trees

TL;DR

This paper provides exact formulas for algebraic invariants such as depth, Stanley depth, projective dimension, regularity, and Krull dimension of the quotient of a polynomial ring by the edge ideal of perfect semiregular trees.

Contribution

It introduces explicit formulas for key invariants of residue class rings of edge ideals associated with perfect semiregular trees, advancing understanding of their algebraic structure.

Findings

Formulas for depth and Stanley depth

Formulas for projective dimension and regularity

Formulas for Krull dimension

Abstract

Let S be a polynomial algebra over a field. If I is the edge ideal of a perfect semiregular tree, then we give precise formulas for values of depth, Stanley depth, projective dimension, regularity and Krull dimension of S/I.