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

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

2009-10-16

arxiv.org/abs/0910.3193v2

Mathematics

Combinatorics

17 pages

Scientific paper

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 \pi,\sigma in S, there is a projective point p in P_q such that p^\pi=p^\sigma. 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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