Luis A. Dupont and Daniel G. Mendoza: On the Stanley depth of edge ideals of k-partite clutters, p.39-49

Abstract:

We give upper bounds for the Stanley depth of edge ideals of certain $k$-partite clutters. In particular, we generalize a result of Ishaq about the Stanley depth of the edge ideal of a complete bipartite graph. A result of Pournaki, Seyed Fakhari and Yassemi implies that the Stanley's conjecture holds for d-uniform complete d-partite clutters. Here we give a shorter and different proof of this fact.

Key Words: Monomial ideal, Stanley's conjecture, Stanley decompositions, Stanley depth.

2000 Mathematics Subject Classification: Primary: 13A15,
Secondary: 05E40.