Noun
a square matrix of n rows and columns; cells contain n different symbols so arranged that no symbol occurs more than once in any row or column
Source: WordNetConversely, every Latin square can be taken as the multiplication table of a quasigroup in many ways: the border row (containing the column headers) and the border column (containing the row headers) can each be any permutation of the elements. Source: Internet
For any Latin square, there are n 2 triples since choosing any two uniquely determines the third. Source: Internet
For example, the Latin square above is not reduced because its first column is A, C, B rather than A, B, C. Any Latin square can be reduced by permuting (that is, reordering) the rows and columns. Source: Internet
If we systematically and consistently reorder the three items in each triple, another orthogonal array (and, thus, another Latin square) is obtained. Source: Internet
Equivalence classes of Latin squares Many operations on a Latin square produce another Latin square (for example, turning it upside down). Source: Internet
If we permute the rows, permute the columns, and permute the names of the symbols of a Latin square, we obtain a new Latin square said to be isotopic to the first. Source: Internet