Weakly stable ideals (Q1382126)

Stable ideals are some monomial ideals introduced by \textit{S. Eliahou} and \textit{M. Kervaire} [J. Algebra 129, No. 1, 1-25 (1990; Zbl 0701.13006)], who gave explicitly their minimal free resolutions. These resolutions are linear if we consider only stable ideals generated by monomials of the same degree. The present paper introduces a class of squarefree monomial ideals, the so called weakly stable ideals, for which there exist still nice formulas for graded Betti numbers. For weakly stable ideals \(I\) generated by monomials of the same degree the authors give explicitly the minimal free resolutions, which are still linear. These resolutions are subcomplexes of the minimal free resolutions of the stable closure of \(I\).