An Omission in Norton's List of $7 \times 7$ Squares
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This article is published in Annals of Mathematical Statistics.The article was published on 1951-06-01 and is currently open access. It has received 33 citations till now.read more
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Small latin squares, quasigroups, and loops
TL;DR: In this paper, Combin et al. presented the number of isotopy classes and main classes of Latin squares, and the numbers of isomorphism classes of quasigroups and loops up to order 10.
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The number of Latin squares of order 11
TL;DR: The enumeration is constructive for the main classes with an autoparatopy group of order at least 3 and isomorphism classes of quasigroups of order 11.
Journal ArticleDOI
The number of Latin squares of order 11
TL;DR: In this paper, constructive and non-constructive techniques are employed to enumerate Latin squares and related objects, and it is established that there are (i) 2036029552582883134196099 main classes of Latin squares of order 11; (ii) 6108088657705958932053657 isomorphism classes of one-factorizations of K 11,11 ; (iii) 12216177315369229261482540 isotopy classes of normal Latin squares; (iv) 14781574551580444528
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On the number of 8 x 8 Latin squares
TL;DR: This work finds numbers that agree with Wells, but different from those of Brown and Arlazarov and coworkers, and gives the distributions of these numbers according to the size of the automorphism group, which allows one to easily cross check the results.