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Martin Klazar

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Martin Klazar

Two results on a partial ordering of nite sequences

Comment.Math.Univ.Carolinae 34,4 (1993) 697-705.

Abstract: In the first part of the paper we are concerned about finite sequences (over arbitrary symbols) u for which Ex(u, n) = O(n). The function Ex(u, n) measures the maximum length of finite sequences overnsymbols which contain no subsequence of the typeu. It follows from the result of Hart and Sharir that the containmentababa≺uis a (minimal) obstacle to Ex(u, n) =O(n). We show by means of a construction due to Sharir and Wiernik that there is another obstacle to the linear growth.

In the second part of the paper we investigate whether the above containment of sequences is wqo. It is trivial that it is not but we show that the smaller family of sequences whose alternate graphs contain nok-path is well quasiordered by that containment.

Keywords: : Davenport-Schinzel sequence, extremal problem, linear growth, min- imal obstacle to linearity, well quasiordering, alternate graph

AMS Subject Classification: 05D99, 06A07

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