How many 7 × 7 latin squares can be partitioned into Youden squares?
نویسندگان
چکیده
منابع مشابه
How Many Squares Can a String Contain?
All our words (strings) are over a fixed alphabet. A square is a subword of the form uu=u, where u is a nonempty word. Two squares are distinct if they are of different shape, not just translates of each other. A word u is primitive if u cannot be written in the form u=v j for some j 2. A square u with u primitive is primitive rooted. Let M(n) denote the maximum number of distinct squares, P(n)...
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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.
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A k_n Latin rectangle is a k_n matrix of entries from [1, 2, ..., n] such that no symbol occurs twice in any row or column. An intercalate is a 2_2 Latin subrectangle. Let N(R) be the number of intercalates in R, a randomly chosen k_n Latin rectangle. We obtain a number of results about the distribution of N(R) including its asymptotic expectation and a bound on the probability that N(R)=0. For...
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Counting the types of squares rather than their occurrences, we consider the problem of bounding the number of distinct squares in a string. In 1998 Fraenkel and Simpson showed that a string of length n contains at most 2n distinct squares. In 2007 Ilie provided an asymptotic upper bound of 2n−Θ(log n). We show that a string of length n contains at most b5n/3c distinct squares. This new upper b...
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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00216-6