Some properties of Davenport-Schinzel sequences
نویسندگان
چکیده
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 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 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 کاملSources of Superlinearity in Davenport-Schinzel Sequences
A generalized Davenport-Schinzel sequence is one over a finite alphabet that contains no subsequences isomorphic to a fixed forbidden subsequence. One of the fundamental problems in this area is bounding (asymptotically) the maximum length of such sequences. Following Klazar, let Ex(σ, n) be the maximum length of a sequence over an alphabet of size n avoiding subsequences isomorphic to σ. It ha...
متن کاملCombinatorial aspects of Davenport-Schinzel sequences
A finite sequence u = a1a2 . . . ap of some symbols is contained in another sequence v = b1b2 . . . bq if there is a subsequence bi1bi2 . . . bip of v which can be identified, after an injective renaming of symbols, with u. We say that u = a1a2 . . . ap is k-regular if i − j ≥ k whenever ai = aj , i > j. We denote further by |u| the length p of u and by ‖u‖ the number of different symbols in u....
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1971
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-17-4-355-362