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

University of Haifa

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	American 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

Keywords

Generating function
harmonic number
initial longest increasing sequence
permutation

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.26493/2590-9770.1516.96f

Cite this

@article{f96de7dcaf854297a2c46292e944ffc1,

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 → ∞.",

keywords = "Generating function, harmonic number, initial longest increasing sequence, permutation",

author = "Toufik Mansour",

year = "2023",

doi = "10.26493/2590-9770.1516.96f",

language = "American English",

volume = "6",

journal = "Art of Discrete and Applied Mathematics",

issn = "2590-9770",

publisher = "University of Primorska",

number = "3",

}

TY - JOUR

T1 - The length of the initial longest increasing sequence in a permutation

AU - Mansour, Toufik

PY - 2023

Y1 - 2023

N2 - 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 → ∞.

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

UR - http://www.scopus.com/inward/record.url?scp=85170844506&partnerID=8YFLogxK

U2 - 10.26493/2590-9770.1516.96f

DO - 10.26493/2590-9770.1516.96f

M3 - Article

SN - 2590-9770

VL - 6

JO - Art of Discrete and Applied Mathematics

JF - Art of Discrete and Applied Mathematics

IS - 3

M1 - P3.05

ER -

The length of the initial longest increasing sequence in a permutation

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this