Permutations with equal orders

Huseyin Acan; Charles Burnette; Sean Eberhard; Eric Schmutz; James Thomas

doi:10.1017/S0963548321000043

Permutations with equal orders

Huseyin Acan
, Charles Burnette
, Sean Eberhard
, Eric Schmutz^*
, James Thomas

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

Let P(ord π = ord π') be the probability that two independent, uniformly random permutations of [n] have the same order. Answering a question of Thibault Godin, we prove that P(ord π = ord π') = n⁻2+o(1) and that P(ord π = ord π') > ¹₂ n⁻² lg* n for infinitely many n. (Here lg* n is the height of the tallest tower of twos that is less than or equal to n.).

Original language	English
Pages (from-to)	800 - 810
Journal	Combinatorics Probability and Computing
Early online date	27 Jan 2021
DOIs	https://doi.org/10.1017/S0963548321000043
Publication status	Published - Sept 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press.

ASJC Scopus subject areas

Theoretical Computer Science
Statistics and Probability
Computational Theory and Mathematics
Applied Mathematics

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10.1017/S0963548321000043Licence: Unspecified

Cite this

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title = "Permutations with equal orders",

abstract = "Let P(ord π = ord π') be the probability that two independent, uniformly random permutations of [n] have the same order. Answering a question of Thibault Godin, we prove that P(ord π = ord π') = n−2+o(1) and that P(ord π = ord π') > 12 n−2 lg* n for infinitely many n. (Here lg* n is the height of the tallest tower of twos that is less than or equal to n.).",

author = "Huseyin Acan and Charles Burnette and Sean Eberhard and Eric Schmutz and James Thomas",

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AU - Acan, Huseyin

AU - Burnette, Charles

AU - Eberhard, Sean

AU - Schmutz, Eric

AU - Thomas, James

PY - 2021/9

Y1 - 2021/9

N2 - Let P(ord π = ord π') be the probability that two independent, uniformly random permutations of [n] have the same order. Answering a question of Thibault Godin, we prove that P(ord π = ord π') = n−2+o(1) and that P(ord π = ord π') > 12 n−2 lg* n for infinitely many n. (Here lg* n is the height of the tallest tower of twos that is less than or equal to n.).

AB - Let P(ord π = ord π') be the probability that two independent, uniformly random permutations of [n] have the same order. Answering a question of Thibault Godin, we prove that P(ord π = ord π') = n−2+o(1) and that P(ord π = ord π') > 12 n−2 lg* n for infinitely many n. (Here lg* n is the height of the tallest tower of twos that is less than or equal to n.).

U2 - 10.1017/S0963548321000043

DO - 10.1017/S0963548321000043

M3 - Article

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SN - 0963-5483

SP - 800

EP - 810

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

ER -

Permutations with equal orders

Abstract

Bibliographical note

ASJC Scopus subject areas

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