ORTHOGONAL PARTITIONS OF THE 6times6 LATIN SQUARES
نویسندگان
چکیده
منابع مشابه
Indivisible partitions of latin squares
In a latin square of order n, a k-plex is a selection of kn entries in which each row, column and symbol occurs k times. A 1-plex is also called a transversal. An indivisible k-plex is one that contains no c-plex for 0ocok. For orders n= 2f2,6g, existence of latin squares with a partition into 1-plexes was famously shown in 1960 by Bose, Shrikhande and Parker. A main result of this paper is tha...
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A Latin square of order n is an n by n array in which every row and column is a permutation of a set N of n elements. Let L = [li,j ] and M = [mi,j ] be two Latin squares of even order n, based on the same N -set. Define the superposition of L onto M to be the n by n array A = (li,j ,mi,j). When n is even, L and M are said to be nearly orthogonal if the superposition of L onto M has every order...
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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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ژورنال
عنوان ژورنال: Annals of Eugenics
سال: 1946
ISSN: 2050-1420
DOI: 10.1111/j.1469-1809.1946.tb02357.x