A new proof for the Erdős–Ko–Rado theorem for the alternating group

A subset S of the alternating group on n points is intersecting if for any pair of permutations π , σ in S , there is an element i ∈ { 1 , … , n } such that π ( i ) = σ ( i ) . We prove if n ≥ 5 and S is intersecting, then | S | ≤ ( n − 1 ) ! 2 . Also, we prove that provided that n ≥ 5 , then the only sets S that meet this bound are the cosets of the stabilizer of a point of { 1 , … , n } . These two results were first proven by Ku and Wong (2007), the proof given in this paper uses an algebraic method that is very different from the original proof.