Improved lower bounds on the length of Davenport-Schinzel sequences

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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].

Original languageEnglish
Pages (from-to)117-124
Number of pages8
JournalCombinatorica
Volume8
Issue number1
DOIs
StatePublished - Mar 1988

Keywords

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

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