Erdos-Ko-Rado theorems for simplicial complexes

Details Erdos-Ko-Rado theorems for simplicial complexes Erdos-Ko-Rado theorems for simplicial complexes

2010-01-04

arxiv.org/abs/1001.0313v3

J. Combin. Theory Ser. A 118 (2011), no. 4, 1218-1227

Mathematics

Combinatorics

14 pages; v2 has minor changes; v3 has further minor changes for publication

Scientific paper

10.1016/j.jcta.2010.11.022

A recent framework for generalizing the Erdos-Ko-Rado Theorem, due to Holroyd, Spencer, and Talbot, defines the Erdos-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 Erdos-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.

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