Separators - a new statistic for permutations

Eli Bagno; Estrella Eisenberg; Shulamit Reches; Moriah Sigron

Separators - a new statistic for permutations

Combinatorics 2019-05-30 v1

Authors: Eli Bagno , Estrella Eisenberg , Shulamit Reches , Moriah Sigron

Abstract

A digit $\pi_j$ in a permutation $\pi=[\pi_1,\ldots,\pi_n]\in S_n$ 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.

Keywords

permutations

Cite

@article{arxiv.1905.12364,
  title  = {Separators - a new statistic for permutations},
  author = {Eli Bagno and Estrella Eisenberg and Shulamit Reches and Moriah Sigron},
  journal= {arXiv preprint arXiv:1905.12364},
  year   = {2019}
}

Separators - a new statistic for permutations

Abstract

Keywords

Cite

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