Stanley depth of weakly polymatroidal ideals and squarefree monomial ideals

الأصل · EN

Let I be a weakly polymatroidal ideal or a squarefree monomial ideal of a polynomial ring S. In this paper we provide a lower bound for the Stanley depth of I and S/I. In particular we prove that if I is a squarefree monomial ideal which is generated in a single degree, then sdepth(I)≥ n-ℓ(I)+1 and sdepth(S/I)≥ n-ℓ(I), where ℓ(I) denotes the analytic spread of I. This proves a conjecture of the author in a special case.