2010/01/31 by Russ Woodroofe · 1 citation
Mathematics · #math.CO #msc:05E45 #msc:05D05
paper · pdf · doi:10.1016/j.jcta.2010.11.022
published as J. Combin. Theory Ser. A 118 (2011), no. 4, 1218-1227 · 14 pages; v2 has minor changes; v3 has further minor changes for publication
arxiv created 2010/11/29 · arxiv updated 2011/01/27
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.