Davenport-Schinzel theory of matrices
نویسندگان
چکیده
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) = @(cY(n)n), where o(n) is the inverse of the Ackermann function.
منابع مشابه
Degrees of nonlinearity in forbidden 0-1 matrix problems
A 0-1 matrix A is said to avoid a forbidden 0-1 matrix (or pattern) P if no submatrix of A matches P , where a 0 in P matches either 0 or 1 in A. The theory of forbidden matrices subsumes many extremal problems in combinatorics and graph theory such as bounding the length of Davenport-Schinzel sequences and their generalizations, Stanley and Wilf’s permutation avoidance problem, and Turán-type ...
متن کاملGeneralized Davenport–Schinzel sequences: results, problems, and applications
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.
متن کاملLower Bounds on Davenport-Schinzel Sequences via Rectangular Zarankiewicz Matrices
An order-s Davenport-Schinzel sequence over an n-letter alphabet is one avoiding immediate repetitions and alternating subsequences with length s+2. The main problem is to determine the maximum length of such a sequence, as a function of n and s. When s is fixed this problem has been settled (see Agarwal, Sharir, and Shor [1], Nivasch [12] and Pettie [15]) but when s is a function of n, very li...
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 کامل8. 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 103 شماره
صفحات -
تاریخ انتشار 1992