Introduction: For a standard graded k-algebra A = ⊕ n≥0 An let H(A, t) = ∑ n≥0 dimk Ant n be its Hilbert-series. By classical results H(A, t) = hA(t) (1−t)d is a rational function, where d is the Krull dimension of A and hA(t) = h0 + · · ·+hrt a polynomial with integer coefficients with h0 = 1. Since the work of Stanley (see e.g. [41], [37]) in the 70’s enumerative properties of the coefficient...

We answer positively a question of Asia Rauf for the case of intersections of three prime ideals generated by disjoint sets of variables and we present several inequalities on Stanley depth. This is a detailed presentation of our talk at the conference on ”Fundamental structures of algebra” in honor of Prof. Serban Basarab at his 70-th anniversary. Let S = K[x1, . . . , xn] be a polynomial alge...

Let Σ be a finite regular cell complex with ∅ ∈ Σ, and regard it as a poset (i.e., partially ordered set) by inclusion. Let R be the incidence algebra of the poset Σ over a field k. Corresponding to the Verdier duality for constructible sheaves on Σ, we have a dualizing complex ω ∈ Db(modR⊗kR) giving a duality functor from Db(modR) to itself. This duality is somewhat analogous to the Serre dual...