An Algorithm to Compute the Stanley Depth of Monomial Ideals

Let K be a field, S = K[x1, . . . ,xn] be the polynomial ring in n variables with coefficient in K and M be a finitely generated Zn-graded S-module. Let u ∈M be a homogeneous element in M and Z a subset of the set of variables {x1, . . . ,xn}. We denote by uK[Z] the K-subspace of M generated by all elements uv where v is a monomial in K[Z]. If uK[Z] is a free K[Z]-module, the Zn-graded K-space uK[Z]⊂M is called a Stanley space of dimension |Z|. A Stanley decomposition of M is a presentation of the Zn-graded K-module M as a finite direct sum of Stanley spaces