A new proof of the Erdős-Ko-Rado theorem for intersecting families of permutations

  • Authors:

  • Chris Godsil;Karen Meagher

  • Affiliations:

  • Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada;Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2009

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Abstract

Let S(n) be the symmetric group on n points. A subset S of S(n) is intersecting if for any pair of permutations @p,@s in S there is a point i@?{1,...,n} such that @p(i)=@s(i). Deza and Frankl [P. Frankl, M. Deza, On the maximum number of permutations with given maximal or minimal distance, J. Combin. Theory Ser. A 22 (3) (1977) 352-360] proved that if S@?S(n) is intersecting then |S|@?(n-1)!. Further, Cameron and Ku [P.J. Cameron, C.Y. Ku, Intersecting families of permutations, European J. Combin. 24 (7) (2003) 881-890] showed that the only sets that meet this bound are the cosets of a stabilizer of a point. In this paper we give a very different proof of this same result.