Linear resolutions of t-spread lexsegment ideals via Betti splittings

Abstract

Let [Formula: see text] be a polynomial ring in [Formula: see text] variables with coefficients over a field [Formula: see text]. A [Formula: see text]-spread lexsegment ideal [Formula: see text] of [Formula: see text] is a monomial ideal generated by a [Formula: see text]-spread lexsegment set. We determine all [Formula: see text]-spread lexsegment ideals with linear resolution by means of Betti splittings. As applications we provide formulas for the Betti numbers of such a class of ideals and furthermore we characterize all incompletely [Formula: see text]-spread lexsegment ideals with linear quotients.