The number of Latin squares of order 11

The number of Latin squares of order 11

Constructive and nonconstructive techniques are employed to enumerate Latin squares and related objects. It is established that there are (i) 2036029552582883134196099 main classes of Latin squares of order 11; (ii) 6108088657705958932053657 isomorphism classes of one-factorizations of K11,11; (iii) 12216177315369229261482540 isotopy classes of Latin squares of order 11; (iv) 147815745515804445...

Latin 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

On the Number of Latin Squares

We (1) determine the number of Latin rectangles with 11 columns and each possible number of rows, including the Latin squares of order 11, (2) answer some questions of Alter by showing that the number of reduced Latin squares of order n is divisible by f ! where f is a particular integer close to 1 2 n, (3) provide a formula for the number of Latin squares in terms of permanents of (+1, −1)-mat...

Determinants of Latin Squares of Order 8

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.