Cellular structure for the Herzog--Takayama Resolution

TL;DR

This paper proves that the Herzog--Takayama resolution for ideals with regular linear quotients is cellular, extending known cellularity results to a broader class of algebraic objects.

Contribution

It demonstrates that the Herzog--Takayama resolution is cellular for ideals with regular linear quotients, including matroidal and stable ideals.

Findings

Herzog--Takayama resolution is cellular for these ideals.

Extends cellularity property to a broader class of resolutions.

Supports the understanding of algebraic and combinatorial structures.

Abstract

Herzog and Takayama constructed explicit resolutions for the class of so called ideals with a regular linear quotient. This class contains all matroidal and stable ideals. The resolutions of matroidal and stable ideals are known to be cellular. In this note we show that the Herzog--Takayama resolution is also cellular.