If a pure simplicial complex is partitionable, then its h-vector has combinatorial interpretation in terms of any partitioning the complex. Given non-partitionable Δ, we construct Γ⊇Δ same dimension such that both Γ and relative (Γ,Δ) are partitionable. This allows us to rewrite as difference two h-vectors partitionable complexes, giving an analogous By contrast, for given Δ it not always possi...

Let R be a commutative Noetherian ring. The k-torsionless modules are defined in [7] as a generalization of torsionless and reflexive modules, i.e., torsionless modules are 1-torsionless and reflexive modules are 2-torsionless. Some properties of torsionless, reflexive, and k-torsionless modules are investigated in this paper. It is proved that if M is an R-module such that G-dimR(M)