Separators - a new statistic for permutations

Separators - a new statistic for permutations

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 $S_n$. W...

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Hauptverfasser: Bagno, Eli, Eisenberg, Estrella, Reches, Shulamit, Sigron, Moriah
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creator Bagno, Eli
Eisenberg, Estrella
Reches, Shulamit
Sigron, Moriah
description 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.
doi_str_mv 10.48550/arxiv.1905.12364
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title Separators - a new statistic for permutations
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