Periodic de Bruijn triangles: Exact and asymptotic results

Boris Shapiro; Michael Shapiro; Alek Vainshtein

doi:10.1016/j.disc.2004.07.020

Periodic de Bruijn triangles: Exact and asymptotic results

Boris Shapiro, Michael Shapiro, Alek Vainshtein

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

Abstract

We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution.

Original language	English
Pages (from-to)	321-333
Number of pages	13
Journal	Discrete Mathematics
Volume	298
Issue number	1-3
DOIs	https://doi.org/10.1016/j.disc.2004.07.020
State	Published - 6 Aug 2005

Bibliographical note

Funding Information:
The authors are grateful to Max–Planck-Institut für Mathematik, Bonn for its hospitality in Summer 2000 and to the Royal Institute of Technology, Stockholm for the financial support of the visit of A.V. to Stockholm in July–August 2001. Sincere thanks go to R. Ehrenborg, A. Laptev, H. Shapiro, A. Volberg and P. Yuditski for useful discussions.

Keywords

Asymptotics
Generating function
Permutations
Up-down sequence

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2004.07.020

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title = "Periodic de Bruijn triangles: Exact and asymptotic results",

abstract = "We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution.",

keywords = "Asymptotics, Generating function, Permutations, Up-down sequence",

author = "Boris Shapiro and Michael Shapiro and Alek Vainshtein",

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AU - Vainshtein, Alek

N1 - Funding Information: The authors are grateful to Max–Planck-Institut für Mathematik, Bonn for its hospitality in Summer 2000 and to the Royal Institute of Technology, Stockholm for the financial support of the visit of A.V. to Stockholm in July–August 2001. Sincere thanks go to R. Ehrenborg, A. Laptev, H. Shapiro, A. Volberg and P. Yuditski for useful discussions.

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N2 - We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution.

AB - We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution.

KW - Asymptotics

KW - Generating function

KW - Permutations

KW - Up-down sequence

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JO - Discrete Mathematics

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ER -

Periodic de Bruijn triangles: Exact and asymptotic results

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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