Greco-Latin square

Greco-Latin square

English

Noun

Greco-Latin square (plural Greco-Latin squares)

1. The superposition of two Latin squares such that the result is also a Latin square.
   • 2013, Natalia Juristo, ‎Ana M. Moreno, Basics of Software Engineering Experimentation, page 381:

     Bose and Shrikhande then applied these rules and were able to build a Greco-Latin square of order 22. This disproved Euler's conjecture, as 22 is an even number not divisible by four.

   • 2018, Reza Hoshmand, Design of Experiments for Agriculture and the Natural Sciences, page 48:

     Table 3.3.3.1 shows a Greco-Latin square with four treatments.

   • 2012, Jason Rosenhouse, ‎Laura Taalman, Taking Sudoku Seriously, page 43:

     Since we now have repeated ordered pairs, the square above is not a Greco-Latin square.

Example

Given the following two Latin Squares:

A B C
B C A
C A B

and

a b c
c a b
b c a

the resultant Greco-Latin square is

Aa Bb Cc
Bc Ca Ab
Cb Ac Ba