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

2009/10/16 by Karen Meagher, Pablo Spiga, Meagher, Karen +1
Mathematics · #05C35 #05C69 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT #msc:05C35 #msc:05C69

paper · pdf · doi:10.48550/arxiv.0910.3193

17 pages

arxiv created 2010/10/21 · arxiv updated 2010/10/22

Abstract

Let G=PGL(2,q) be the projective general linear group acting on the projective line P_q. A subset S of G is intersecting if for any pair of permutations π,σin S, there is a projective point p in P_q such that p^π=p^σ. We prove that if S is intersecting, then the size of S is no more than q(q-1). Also, we prove that the only sets S that meet this bound are the cosets of the stabilizer of a point of P_q.

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