Separators - a new statistic for permutations

Abstract

A digit ${\pi }_j$ in a permutation $\pi =[{\pi }_1,\dots ,{\pi }_n]\in S_n$ is defined to be a separator of $\pi$ if by omitting it from $\pi$ we get a new $2-$block. In this work we introduce a new statistic, the number of separators, on the symmetric group $S_n$ and calculate its distribution over $S_n$. We also provide some enumerative and asymptotic results regarding this statistic.

Cited by in corpus (2)

• Counting King Permutations on the Cylinder
• The poset of king permutations on a cylinder