Note on enumeration of $ 7 \times 7 $ Latin Squares
نویسندگان
چکیده
منابع مشابه
2 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.
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The enumeration of self-orthogonal Latin squares (SOLS) of a given order seems to be an open problem in the literature on combinatorial designs. The existence of at least one SOLS is guaranteed for any order except 2, 3 and 6, but it is not known how many of these squares of a given order exist. In this talk we present enumeration tables of unequal SOLS, idempotent SOLS, isomorphism classes of ...
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We give a condition on the spatial distribution of filled cells in a partial Latin square P that is sufficient to ensure completability, regardless of what symbols are used in the filled cells. For example, if P is of the order mr + t, where m, r are positive integers and t ≥ 0, m is odd, and the filled cells of P are contained in the first m+1 2 r × r subsquares along the main diagonal, our co...
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ژورنال
عنوان ژورنال: Bulletin of Mathematical Statistics
سال: 1952
ISSN: 0007-4993
DOI: 10.5109/12951