The length of the initial longest increasing sequence in a permutation

Toufik Mansour

doi:10.26493/2590-9770.1516.96f

The length of the initial longest increasing sequence in a permutation

Toufik Mansour

Department of Mathematics

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

Abstract

Let S_n be the set of all permutations of {1, 2, . . ., n} represented in cycle notation. Define a_n,m to be the number of π ∈ S_n such that the length of the initial longest increasing sequence (ILIS) in π is at most m. For fixed m, we find the exponential generating function for the sequence a_n,m, and give an asymptotic formula for a_n,m when n → ∞.

Original language	English
Article number	P3.05
Journal	Art of Discrete and Applied Mathematics
Volume	6
Issue number	3
DOIs	https://doi.org/10.26493/2590-9770.1516.96f
State	Published - 2023

Bibliographical note

Publisher Copyright:
© 2023 Societa Editrice il Mulino. All rights reserved.

Keywords

Generating function
harmonic number
initial longest increasing sequence
permutation

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.26493/2590-9770.1516.96f

Cite this

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title = "The length of the initial longest increasing sequence in a permutation",

abstract = "Let Sn be the set of all permutations of {1, 2, . . ., n} represented in cycle notation. Define an,m to be the number of π ∈ Sn such that the length of the initial longest increasing sequence (ILIS) in π is at most m. For fixed m, we find the exponential generating function for the sequence an,m, and give an asymptotic formula for an,m when n → ∞.",

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AB - Let Sn be the set of all permutations of {1, 2, . . ., n} represented in cycle notation. Define an,m to be the number of π ∈ Sn such that the length of the initial longest increasing sequence (ILIS) in π is at most m. For fixed m, we find the exponential generating function for the sequence an,m, and give an asymptotic formula for an,m when n → ∞.

KW - Generating function

KW - harmonic number

KW - initial longest increasing sequence

KW - permutation

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The length of the initial longest increasing sequence in a permutation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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