The infinite limit of separable permutations

Ross G. Pinsky

doi:10.1002/rsa.21014

The infinite limit of separable permutations

Ross G. Pinsky

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Let (Formula presented.) denote the uniform probability measure on the set of separable permutations in S_n. Let (Formula presented.) with an appropriate metric and denote by (Formula presented.) the compact metric space consisting of functions (Formula presented.) from (Formula presented.) to (Formula presented.) which are injections when restricted to (Formula presented.); that is, if (Formula presented.), i ≠ j, then (Formula presented.). Extending permutations (Formula presented.) by defining (Formula presented.), for j > n, we have (Formula presented.). We show that (Formula presented.) converges weakly on (Formula presented.) to a limiting distribution of regenerative type, which we calculate explicitly.

Original language	English
Article number	4
Pages (from-to)	622-639
Number of pages	18
Journal	Random Structures and Algorithms
Volume	59
Issue number	4
DOIs	https://doi.org/10.1002/rsa.21014
State	Published - 2021

Keywords

Schröder numbers
random permutation
separable permutations

All Science Journal Classification (ASJC) codes

Software
Applied Mathematics
General Mathematics
Computer Graphics and Computer-Aided Design

Access to Document

10.1002/rsa.21014

Cite this

@article{bde07e14b23445aca1d5bc9e7884c9ba,

title = "The infinite limit of separable permutations",

abstract = "Let (Formula presented.) denote the uniform probability measure on the set of separable permutations in Sn. Let (Formula presented.) with an appropriate metric and denote by (Formula presented.) the compact metric space consisting of functions (Formula presented.) from (Formula presented.) to (Formula presented.) which are injections when restricted to (Formula presented.); that is, if (Formula presented.), i ≠ j, then (Formula presented.). Extending permutations (Formula presented.) by defining (Formula presented.), for j > n, we have (Formula presented.). We show that (Formula presented.) converges weakly on (Formula presented.) to a limiting distribution of regenerative type, which we calculate explicitly.",

keywords = "Schr{\"o}der numbers, random permutation, separable permutations",

author = "Pinsky, {Ross G.}",

note = "Publisher Copyright: {\textcopyright} 2021 Wiley Periodicals LLC.",

year = "2021",

doi = "10.1002/rsa.21014",

language = "الإنجليزيّة",

volume = "59",

pages = "622--639",

journal = "Random Structures and Algorithms",

issn = "1042-9832",

publisher = "John Wiley and Sons Ltd",

number = "4",

}

TY - JOUR

T1 - The infinite limit of separable permutations

AU - Pinsky, Ross G.

PY - 2021

Y1 - 2021

N2 - Let (Formula presented.) denote the uniform probability measure on the set of separable permutations in Sn. Let (Formula presented.) with an appropriate metric and denote by (Formula presented.) the compact metric space consisting of functions (Formula presented.) from (Formula presented.) to (Formula presented.) which are injections when restricted to (Formula presented.); that is, if (Formula presented.), i ≠ j, then (Formula presented.). Extending permutations (Formula presented.) by defining (Formula presented.), for j > n, we have (Formula presented.). We show that (Formula presented.) converges weakly on (Formula presented.) to a limiting distribution of regenerative type, which we calculate explicitly.

AB - Let (Formula presented.) denote the uniform probability measure on the set of separable permutations in Sn. Let (Formula presented.) with an appropriate metric and denote by (Formula presented.) the compact metric space consisting of functions (Formula presented.) from (Formula presented.) to (Formula presented.) which are injections when restricted to (Formula presented.); that is, if (Formula presented.), i ≠ j, then (Formula presented.). Extending permutations (Formula presented.) by defining (Formula presented.), for j > n, we have (Formula presented.). We show that (Formula presented.) converges weakly on (Formula presented.) to a limiting distribution of regenerative type, which we calculate explicitly.

KW - Schröder numbers

KW - random permutation

KW - separable permutations

UR - http://www.scopus.com/inward/record.url?scp=85106306435&partnerID=8YFLogxK

U2 - 10.1002/rsa.21014

DO - 10.1002/rsa.21014

M3 - مقالة

SN - 1042-9832

VL - 59

SP - 622

EP - 639

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 4

M1 - 4

ER -

The infinite limit of separable permutations

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this