The EKR property for flag pure simplicial complexes without boundary

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:172

Article

Olarte, Jorge Alberto¹  Santos, Francisco²  Spreer, Jonathan³  Stump, Christian⁴ 

[1] Rhein Westfal TH Aachen, Lehrstuhl B Math, Aachen, Germany

[2] Univ Cantabria, Dept Math Stat & Comp Sci, Cantabria, Spain

[3] Univ Sydney, Sch Math & Stat F07, Sydney, NSW 2006, Australia

[4] Ruhr Univ Bochum, Fak Math, Bochum, Germany

关键词: Erdos-Ko-Rado property;    EKR;    Flag (pseudo-)manifolds;    Cluster complexes;    Simplicial complexes;   

DOI  :  10.1016/j.jcta.2019.105205

来源: Elsevier

【 摘 要 】

We prove that the family of facets of a pure simplicial complex C of dimension up to three satisfies the Erdos-Ko-Rado property whenever C is flag and has no boundary ridges. We conjecture the same to be true in arbitrary dimension and give evidence for this conjecture. Our motivation is that complexes with these two properties include flag pseudo-manifolds and cluster complexes. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free