Completion of the Spectrum of Orthogonal Diagonal Latin Squares

This chapter describes the concept of completion of the spectrum of orthogonal diagonal Latin squares. A diagonal Latin square is one in which both the main diagonal and the main back-diagonal are transversals. It discusses preliminaries of the spectrum of orthogonal diagonal Latin squares as well as previous results. A. J. W. Hilton proved (using a Wilson-type argument) that the number of unconstructed sides was finite, although (as in most arguments of this type, the bound achieved is unconscionably large). The spectrum has recently been completed; there are indeed orthogonal diagonal Latin squares of side 10. After both independent and cooperative work by the six authors, a pair was produced by Fred Cherry and Mel Most in New York, and then independently by John Brown in Urbana.