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

Abstract

A subset $S$ of the alternating group on $n$ points is {\it intersecting} if for any pair of permutations $\pi ,\sigma$ in $S$, there is an element $i\in \{1,\dots ,n\}$ such that $\pi (i)=\sigma (i)$. We prove that if $S$ is intersecting, then $|S|\le \frac{(n-1)!}{2}$. Also, we prove that if $n\ge 5$, then the only sets $S$ that meet this bound are the cosets of the stabilizer of a point of $\{1,\dots ,n\}$.

23 pages