Transversals in long rectangular arrays
نویسندگان
چکیده
منابع مشابه
Transversals in long rectangular arrays
In this paper it is shown that every m× n array in which each symbol appears at most (mn− 1)/(m− 1) times has a transversal, when n 2m3. © 2006 Elsevier B.V. All rights reserved.
متن کاملLatin Transversals in Long Rectangular Arrays
In this paper it is shown that every m×n array in which each symbol appears at most (mn− 1)/(m− 1) times has a latin transversal, when n is large enough in comparison to m.
متن کاملTransversals of Rectangular Arrays
The paper deals with m by n rectangular arrays whose mn cells are filled with symbols. A section of the array consists of m cells, one from each row and no two from the same column. The paper focuses on the existence of sections that do contain symbols with high multiplicity.
متن کاملLatin Transversals of Rectangular Arrays By
Let m and n be integers, 2 ≤ m ≤ n. An m by n array consists of mn cells, arranged in m rows and n columns, and each cell contains exactly one symbol. A transversal of an array consists of m cells, one from each row and no two from the same column. A latin transversal is a transversal in which no symbol appears more than once. We investigte L(m, n), the largest integer such that if each symbol ...
متن کاملPeriodicity in Rectangular Arrays
We discuss several two-dimensional generalizations of the familiar Lyndon-Schützenberger periodicity theorem for words. We consider the notion of primitive array (as one that cannot be expressed as the repetition of smaller arrays). We count the number of m×n arrays that are primitive. Finally, we show that one can test primitivity and compute the primitive root of an array in linear time.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2006
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.02.027