A new proof for the Erdős-Ko-Rado Theorem for the alternating group

الأصل · EN

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 that if S is intersecting, then |S|≤ (n-1)!/2. Also, we prove that if n ≥ 5, then the only sets S that meet this bound are the cosets of the stabilizer of a point of {1,,n}.