A note on minimal resolutions of vector-spread Borel ideals

TL;DR

This paper studies vector-spread Borel ideals, proving they have linear quotients, determining their Betti numbers and Poincaré series, and classifying those that are Cohen-Macaulay.

Contribution

It provides new insights into the structure of vector-spread Borel ideals, including their Betti numbers and Cohen-Macaulay classification.

Findings

Vector-spread Borel ideals have linear quotients.

Explicit formulas for graded Betti numbers and Poincaré series are derived.

A complete classification of Cohen-Macaulay vector-spread Borel ideals is provided.

Abstract

We consider vector-spread Borel ideals. We show that these ideals have linear quotients and thereby we determine the graded Betti numbers and the bigraded Poincar\'e series. A characterization of the extremal Betti numbers of such a class of ideals is given. Finally, we classify all Cohen-Macaulay vector-spread Borel ideals.