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Improved lower bounds on the length of Davenport-Schinzel sequences. (English) Zbl 0672.05015

For the longest length of general Davenport-Schinzel sequences, i.e. sequences of n letters with no immediate repetitions and no subsequence of type a..b..a..b..a.. of length \(s+2\), the estimate \(\Omega (n\alpha^ s(n))\) is established, where \(\alpha\) (n) is the inverse of the Ackermann function. This improves earlier bounds. The proof uses generalized path compression schemes.
Reviewer: P.Komjáth

MSC:

05A99 Enumerative combinatorics
05C35 Extremal problems in graph theory
68Q25 Analysis of algorithms and problem complexity
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