Powers of lexsegment ideals with linear resolution

摘要

All powers of lexsegment ideals with linear resolution (equivalently, withlinear quotients) have linear quotients with respect to suitable orders of theminimal monomial generators. For a large subclass of the lexsegment ideals thecorresponding Rees algebra has a quadratic Gr"obner basis, thus it is Koszul.We also find other classes of monomial ideals with linear quotients whosepowers have linear quotients too.