On the two-dimensional davenport-schinzel problem

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منابع مشابه

8. Davenport-schinzel Sequences

Definition 18.1 A (n, s)-Davenport-Schinzel sequence is a sequence over an alphabet A of size n in which no two consecutive characters are the same and there is no alternating subsequence of the form .

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Generalized Davenport-Schinzel Sequences

The extremal function Ex(u, n) (introduced in the theory of DavenportSchinzel sequences in other notation) denotes for a fixed finite alternating sequence u = ababa . . . the maximum length of a finite sequence v over n symbols with no immediate repetition which does not contain u. Here (following the idea of J. Nešetřil) we generalize this concept for arbitrary sequence u. We summarize the alr...

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On numbers of Davenport-Schinzel sequences

One class of Davenport-Schinzel sequences consists of finite sequences over n symbols without immediate repetitions and without any subsequence of the type abab. We present a bijective encoding of such sequences by rooted plane trees with distinguished nonleaves and we give a combinatorial proof of the formula 1 k − n+ 1 ( 2k − 2n k − n )( k − 1 2n− k − 1 ) for the number of such normalized seq...

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Keywords. Davenport{schinzel Sequence; Tree; Extremal Problem 0 Extremal Problems for Colored Trees and Davenport{schinzel Sequences

In the theory of generalized Davenport{Schinzel sequences one estimates the maximum lengths of nite sequences containing no subsequence of a given pattern. Here we investigate a further generalization, in which the class of sequences is extended to the class of colored trees. We determine exactly the extremal functions associated with the properly 2-colored path of four vertices and with the mo...

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Tightish Bounds on Davenport-Schinzel Sequences

Let Ψs(n) be the extremal function of order-s Davenport-Schinzel sequences over an n-letter alphabet. Together with existing bounds due to Hart and Sharir (s = 3), Agarwal, Sharir, and Shor (s = 4, lower bounds on s ≥ 6), and Nivasch (upper bounds on even s), we give the following essentially tight bounds on Ψs(n) for all s: Ψs(n) =  n s = 1

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ژورنال

عنوان ژورنال: Journal of Symbolic Computation

سال: 1990

ISSN: 0747-7171

DOI: 10.1016/s0747-7171(08)80070-3