LCM Lattices and Stanley Depth: A First Computational Approach

Abstract

Let K be a field, and let S D K [X1, . . . ,Xn] be the polynomial ring. Let / be a monomial ideal of S with up to 5 generators. In this paper, we present a computational experiment which allows us to prove that depthS S / I D sdepthS S / I < sdepthS I. This shows that the Stanley conjecture is true for S/I and I, if I can be generated by at most 5 monomials. The result also brings additional computational evidence for a conjecture made by Herzog.