A pair of latin squares A=(aij) and B=(bij) are orthogonal iff the ordered pairs (aij,bij) are distinct for all i and j. Here are a pair of orthogonal latin squares of order 3. A and B are clearly latin squares and, when superimposed, you can see that all ordered pairs from corresponding square entries are distinct.
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A set of Latin squares, all of the same order, all pairs of which are orthogonal is called a set of mutually orthogonal Latin squares.
Apr 11, 2006 · An arrangement of s elements in s rows and s columns, such that no element repeats more than once in each row and each column is called a Latin square of order ...
Jun 19, 2006 · Abstract: A Latin square arrangement is an arrangement of s symbols in s rows and s columns, such that every symbol occurs once in each.
An orthogonal latin square graph is a graph whose vertices are latin squares of the same order and with adjacency of vertices corresponding to orthogonality of ...
An arrangement of s elements in s rows and s columns, such that no element repeats more than once in each row and each column is called a Latin square of ...
Jul 7, 2021 · A set of Latin squares is mutually orthogonal if every distinct pair of Latin squares in the set are orthogonal. We call such a set, a set of ...
An m-sided Latin square is an arrangement of the numbers 1, 2, • • • , m into m rows and m columns in such a way that no row and no column contains any ...
Dec 11, 2019 · This explains the concept of orthogonality for latin squares, and checks that a certain pair of 4x4 latin squares are orthogonal.
Squares are said to be orthogonal if, when superposed, any symbol of the first square occurs exactly once with each symbol of the second square.