Improved lower bounds on the length of Davenport-Schinzel sequences

Micha Sharir

doi:10.1007/BF02122559

Improved lower bounds on the length of Davenport-Schinzel sequences

Micha Sharir^*

^*Corresponding author for this work

School of Computer Science

New York University

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

11 Scopus citations

Abstract

We derive lower bounds on the maximal length λ_s(n) of (n, s) Davenport Schinzel sequences. These bounds have the form λ_2s=1(n)=Ω(nα^s(n)), where α(n) is the extremely slowly growing functional inverse of the Ackermann function. These bounds extend the nonlinear lower bound λ₃(n)=Ω(nα(n)) due to Hart and Sharir [5], and are obtained by an inductive construction based upon the construction given in [5].

Original language	English
Pages (from-to)	117-124
Number of pages	8
Journal	Combinatorica
Volume	8
Issue number	1
DOIs	https://doi.org/10.1007/BF02122559
State	Published - Mar 1988

Keywords

AMS subject classification (1980): 05A99, 05C35, 68B15

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abstract = "We derive lower bounds on the maximal length λs(n) of (n, s) Davenport Schinzel sequences. These bounds have the form λ2s=1(n)=Ω(nαs(n)), where α(n) is the extremely slowly growing functional inverse of the Ackermann function. These bounds extend the nonlinear lower bound λ3(n)=Ω(nα(n)) due to Hart and Sharir [5], and are obtained by an inductive construction based upon the construction given in [5].",

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AB - We derive lower bounds on the maximal length λs(n) of (n, s) Davenport Schinzel sequences. These bounds have the form λ2s=1(n)=Ω(nαs(n)), where α(n) is the extremely slowly growing functional inverse of the Ackermann function. These bounds extend the nonlinear lower bound λ3(n)=Ω(nα(n)) due to Hart and Sharir [5], and are obtained by an inductive construction based upon the construction given in [5].

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Improved lower bounds on the length of Davenport-Schinzel sequences

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