Complete latin squares of order 2k

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

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.

Some New Row-Complete Latin Squares

A row-complete Latin square (RCLS) of order n, L, is a Latin square in which for any two distinct symbols, X, y, there exist i, j, 1 <i < ~1, 1 <:j < n 1 such that L(i,j) k x and L(i,j I1) =y. Column complete Latin squares are defmed analogously, and a square is complete if it is both. row and column complete. RCLS are used in statistics for the design of sequential experiments. A finite group ...

Atomic Latin Squares of Order Eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i 61⁄4 j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, in...