Erdős–Ko–Rado theorems for simplicial complexes
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- 作者：Russ Woodroofe<sup>asup><sup> ; sup><sup>russw@math.wustl.edusup>
- 关键词：Erdő ; s– ; Ko– ; Rado ; Algebraic shifting ; Cohen– ; Macaulay ; Shellable ; Depth ; Independence complex
- 刊名：Journal of Combinatorial Theory, Series A
- 出版年：2011
- 出版时间：May 2011
- 年：2011
- 卷：118
- 期：4
- 页码：1218-1227
- 全文大小：164 K
文摘
A recent framework for generalizing the Erdős–Ko–Rado theorem, due to Holroyd, Spencer, and Talbot, defines the Erdős–Ko–Rado property for a graph in terms of the graph's independent sets. Since the family of all independent sets of a graph forms a simplicial complex, it is natural to further generalize the Erdős–Ko–Rado property to an arbitrary simplicial complex. An advantage of working in simplicial complexes is the availability of algebraic shifting, a powerful shifting (compression) technique, which we use to verify a conjecture of Holroyd and Talbot in the case of sequentially Cohen–Macaulay near-cones.