Newtonian and Schinzel sequences in a domain
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 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 کاملA Relationship Between Generalized Davenport-Schinzel Sequences and Interval Chains
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...
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...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2009
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2009.03.004