منابع مشابه
Generalized latin squares I
The classical definition of Latin squares is generalized by allowing multiple occurrences of symbols in each row and each column. A perfect (k, I)-Latin square is an N x N array in which any row or column contains every distinct symbol and the symbol at position (i, j) appears exactly k times in the ith row and I times in the jth column, or vice versa. Existence of such squares and the notion o...
متن کاملTransversals in generalized Latin squares
We are seeking a sufficient condition that forces a transversal in a generalized Latin square. A generalized Latin square of order n is equivalent to a proper edge-coloring of Kn,n. A transversal corresponds to a multicolored perfect matching. Akbari and Alipour defined l(n) as the least integer such that every properly edge-colored Kn,n, which contains at least l(n) different colors, admits a ...
متن کامل2 7 M ar 2 00 3 Latin Squares , Partial Latin Squares and its Generalized Quotients
A (partial) Latin square is a table of multiplication of a (partial) quasigroup. Multiplication of a (partial) quasigroup may be considered as a set of triples. We give a necessary and sufficient condition when a set of triples is a quotient of a (partial) Latin square.
متن کاملLifting Redundancy from Latin Squares to Pandiagonal Latin Squares
In the pandiagonal Latin Square problem, a square grid of size N needs to be filled with N types of objects, so that each column, row, and wrapped around diagonal (both up and down) contains an object of each type. This problem dates back to at least Euler. In its specification as a constraint satisfaction problem, one uses the all different constraint. The known redundancy result about all dif...
متن کاملLatin Squares: Transversals and counting of Latin squares
Author: Jenny Zhang First, let’s preview what mutually orthogonal Latin squares are. Two Latin squares L1 = [aij ] and L2 = [bij ] on symbols {1, 2, ...n}, are said to be orthogonal if every ordered pair of symbols occurs exactly once among the n2 pairs (aij , bij), 1 ≤ i ≤ n, 1 ≤ j ≤ n. Now, let me introduce a related concept which is called transversal. A transversal of a Latin square is a se...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)98135-s