An Erdős–Ko–Rado theorem for the derangement graph of PGL(2,q) acting on the projective line

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• 作者：Karen Meagher ; Pablo Spiga
• 关键词：Derangement graph ; Independent sets ; Erd&#x151 ; s– ; Ko– ; Rado theorem
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2011
• 出版时间：February 2011
• 年：2011
• 卷：118
• 期：2
• 页码：532-544
• 全文大小：212 K

文摘

Let G=PGL(2,q) be the projective general linear group acting on the projective line . A subset S of G is intersecting if for any pair of permutations π,σ in S, there is a projective point such that p<sup>πsup>=p<sup>σsup>. We prove that if S is intersecting, then Sq(q−1). Also, we prove that the only sets S that meet this bound are the cosets of the stabilizer of a point of .