Skip to Main content Skip to Navigation
Conference papers

SIF Permutations and Chord-Connected Permutations

Abstract : A stabilized-interval-free (SIF) permutation on [n], introduced by Callan, is a permutation that does not stabilize any proper interval of [n]. Such permutations are known to be the irreducibles in the decomposition of permutations along non-crossing partitions. That is, if $s_n$ denotes the number of SIF permutations on [n], $S(z)=1+\sum_{n\geq1} s_n z^n$, and $F(z)=1+\sum_{n\geq1} n! z^n$, then $F(z)= S(zF(z))$. This article presents, in turn, a decomposition of SIF permutations along non-crossing partitions. Specifically, by working with a convenient diagrammatic representation, given in terms of perfect matchings on alternating binary strings, we arrive at the \emphchord-connected permutations on [n], counted by $\{c_n\}_{n\geq1}$, whose generating function satisfies $S(z)= C(zS(z))$. The expressions at hand have immediate probabilistic interpretations, via the celebrated moment-cumulant formula of Speicher, in the context of the free probability theory of Voiculescu. The probability distributions that appear are the exponential and the complex Gaussian.
Complete list of metadatas

Cited literature [21 references]  Display  Hide  Download

https://hal.inria.fr/hal-01207573
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, October 1, 2015 - 9:28:38 AM
Last modification on : Wednesday, August 7, 2019 - 12:19:22 PM
Long-term archiving on: : Saturday, January 2, 2016 - 10:49:48 AM

File

dmAT0169.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01207573, version 1

Collections

Citation

Natasha Blitvić. SIF Permutations and Chord-Connected Permutations. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.801-814. ⟨hal-01207573⟩

Share

Metrics

Record views

163

Files downloads

1191