The saturation number of c-bounded stable monomial ideals and their powers

摘要

Let S = Kx(1), ... , x(n) be the polynomial ring in n variables over a field K. In this paper, we compute the socle of c-bounded strongly stable ideals and determine the saturation numbers of strongly stable ideals and equigenerated c-bounded strongly stable ideals. We also provide explicit formulas for the saturation number sat(I) of Veronese-type ideals I. Using this formula, we show that sat(Ik) is quasilinear from the beginning, and we determine the quasilinear function explicitly.