TL;DR
This paper introduces Betti-linear monomial ideals, generalizing lattice-linear ideals, and provides a characterization and explicit resolutions for ideals with pure resolutions.
Contribution
It defines Betti-linearity, characterizes it via Tchernev's poset construction, and offers a canonical method for minimal free resolutions of pure monomial ideals.
Findings
Betti-linear ideals generalize lattice-linear ideals.
Characterization of Betti-linearity via poset construction.
Explicit canonical resolutions for pure monomial ideals.
Abstract
We introduce the notion of a Betti-linear monomial ideal, which generalizes the notion of lattice-linear monomial ideal introduced by Clark. We provide a characterization of Betti-linearity in terms of Tchernev's poset construction. As an application we obtain an explicit canonical construction for the minimal free resolutions of monomial ideals having pure resolutions.
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