Stanley decompositions and partitionable simplicial complexes

By Jürgen Herzog, Ali Soleyman Jahan, Siamak Yassemi. 2006

73 citations recorded by the source corpus.

Abstract We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen–Macaulay simplicial complexes. We also prove these conjectures for all Cohen–Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/28e2900f1d2cc90ed576f10eb1dfce36771e1bd0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Asia Rauf
2. Jürgen Herzog
3. Xinxian Zheng
4. Marius Vladoiu
5. Adam Van Tuyl
6. Huy Tài Hà
7. Rafael H. Villarreal
8. Susan Morey

In Discrete Mathematics and Combinatorics

1. Asia Rauf
2. Jürgen Herzog

In Geometry and Topology

1. Asia Rauf
2. Marius Vladoiu
3. Xinxian Zheng
4. Jürgen Herzog
5. Huy Tài Hà
6. Adam Van Tuyl
7. Susan Morey
8. Steven Dale Cutkosky

Citations in the corpus

• How to compute the Stanley depth of a monomial ideal (2007, background): “n fdepthS/I =depthS/I and fdepthI =depthI. In particular, Stanley’s conjecture holds for S/I and I. Proof. The equality fdepthS/I =depthS/I follows from the fact that S/I is pretty clean, as shown in [10]. Let G(I)={u1,...,ur}. In order to compute the fdepth of I we consider the filtration (0)⊂(u1)⊂(”
• Depth and Stanley Depth of Multigraded Modules (2008, background): “The conjecture is discussed in some special cases in [7], [2], [9], [13], [1], [12] [4], [5].”