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 .
متن کاملOn 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...
متن کاملGeneralized 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...
متن کاملKeywords. 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...
متن کاملDavenport-Schinzel theory of matrices
Filredi, Z. and P. Hajnal, Davenport-Schinzel theory of matrices, Discrete Mathematics 103 (1992) 233-251. Let C be a configuration of 1’s. We define f(n; C) to be the maximal number of l’s in a O-l matrix of size n x n not having C as a subconfiguration. We consider the problem of determining the order off (n; C) for several forbidden C’s. Among other results we prove that f (n; (’ 1 ’ J) = @(...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1974
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-25-2-213-224