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:
“This house was designed and constructed with the freedom of stroke of a forester’s axe, without other compass and square than Nature uses.”
—Henry David Thoreau (1817–1862)