Generalized Davenport-Schinzel sequences with linear upper bound
نویسندگان
چکیده
منابع مشابه
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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Let an (r, s)-formation be a concatenation of s permutations of r distinct letters, and let a block of a sequence be a subsequence of consecutive distinct letters. A k-chain on [1,m] is a sequence of k consecutive, disjoint, nonempty intervals of the form [a0, a1][a1 + 1, a2] . . . [ak−1 + 1, ak] for integers 1 6 a0 6 a1 < . . . < ak 6 m, and an s-tuple is a set of s distinct integers. An s-tup...
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Article history: Received 8 August 2010 Available online xxxx
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We survey in detail extremal results on Davenport–Schinzel sequences and their generalizations, from the seminal papers of H. Davenport and A. Schinzel in 1965 to present. We discuss geometric and enumerative applications, generalizations to colored trees, and generalizations to hypergraphs. Eleven illustrative examples with proofs are given and nineteen open problems are posed.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90677-8