منابع مشابه
Subsquare-free Latin squares of odd order
For every odd positive integer m we prove the existence of a Latin square of order 3m having no proper Latin subsquares. Combining this with previously known results it follows that subsquare-free Latin squares exist for all odd orders. © 2005 Elsevier Ltd. All rights reserved.
متن کاملThe construction of subsquare free Latin squares by simulated annealing
A simulated annealing algorithm is used in the construction of subsquare free Latin squares. The algorithm is described and experience from its application is reported. Results obtained include the construction of subsquare free Latin squares of orders 16 and 18, the smallest orders for which existence of such squares was previously in doubt.
متن کاملOn Even and Odd Latin Squares
Latin squares can be classified as odd or even according to the signs of the permutations given by their rows and columns. In this paper, the behaviour of the parities of a latin square under the action of the isotopy group (permuting rows, columns, and symbols) and the transformation group (interchanging rows, columns, and symbols) is analyzed. A rule is given that shows that the behaviour of ...
متن کاملLatin Squares with No Small Odd Plexes
A k-plex in a Latin square of order n is a selection of kn entries in which each row, column, and symbol is represented precisely k times.A transversal of aLatin square corresponds to the case k = 1. We show that for all even n > 2 there exists a Latin square of order n which has no k-plex for any odd k < n4 but does have a k-plex for every other k ≤ 1 2n. © 2008 Wiley Periodicals, Inc. J Combi...
متن کاملLatin Squares of Order 10
We describe two independent computations of the number of Latin squares of order 10. We also give counts of Latin rectangles with up to 10 columns, and estimates of the number of Latin squares of orders up to 15. Mathematics Reviews Subject Classifications: 05B15, 05-04
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2007
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2005.07.002