In mathematics, a Graeco-Latin square or Euler square or orthogonal Latin squares of order n over two sets S and T, each consisting of n symbols, is an n×n arrangement of cells, each cell containing an ordered pair (s,t), where s is in S and t is in T, such that every row and every column contains each element of S and each element of T exactly once, and that no two cells contain the same ordered pair.
The arrangement of the s-coordinates by themselves (which may be thought of as Latin characters) and of the t-coordinates (the Greek characters) each forms a Latin square. A Graeco-Latin square can therefore be decomposed into two "orthogonal" Latin squares. Orthogonality here means that every pair (s, t) from the Cartesian product S×T occurs exactly once.
Read more about Graeco-Latin Square: History, Applications, Mutually Orthogonal Latin Squares
Famous quotes containing the word square:
“If the physicians had not their cassocks and their mules, if the doctors had not their square caps and their robes four times too wide, they would never had duped the world, which cannot resist so original an appearance.”
—Blaise Pascal (1623–1662)