On the two-dimensional davenport-schinzel problem
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 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 کاملTightish 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
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1990
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(08)80070-3