Outline symmetric latin squares

A method for constructing symmetric Hamiltonian double Latin squares

On Some Features of Symmetric Diagonal Latin Squares

In this paper, we study the dependencies of the number of symmetric and doubly symmetric diagonal Latin squares on the order N. Using fast generator of diagonal Latin squares (augmented by symmetry checker), we determined these dependencies for order at most 8. We also found a number of doubly symmetric diagonal Latin squares of orders 12, 16 and 20.

Strongly symmetric self-orthogonal diagonal Latin squares and Yang Hui type magic squares

Keywords: Self-orthogonal Latin square Strongly symmetric Magic square Yang Hui type a b s t r a c t In this paper, a strongly symmetric self-orthogonal diagonal Latin square of order n with a special property (* SSSODLS(n)) is introduced. It is proved that a * SSSODLS(n) exists if and only if n ≡ 0 (mod 4) and n ̸ = 4. As an application, it is shown that there exists a Yang Hui type magic squar...

Lifting Redundancy from Latin Squares to Pandiagonal Latin Squares

In the pandiagonal Latin Square problem, a square grid of size N needs to be filled with N types of objects, so that each column, row, and wrapped around diagonal (both up and down) contains an object of each type. This problem dates back to at least Euler. In its specification as a constraint satisfaction problem, one uses the all different constraint. The known redundancy result about all dif...

Latin Squares: Transversals and counting of Latin squares

Author: Jenny Zhang First, let’s preview what mutually orthogonal Latin squares are. Two Latin squares L1 = [aij ] and L2 = [bij ] on symbols {1, 2, ...n}, are said to be orthogonal if every ordered pair of symbols occurs exactly once among the n2 pairs (aij , bij), 1 ≤ i ≤ n, 1 ≤ j ≤ n. Now, let me introduce a related concept which is called transversal. A transversal of a Latin square is a se...