A note on minimal resolutions of vector–spread Borel ideals

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 Poincaré 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.

Keywords

• monomial ideals
• vector–spread borel ideals
• cohen–macaulay ideals
• extremal betti numbers
• primary 05b35, 05e40, 13b25, 13d02, 68w30