Geodesic
Latin Squares with Prescribed Diagonals
Canadian journal of mathematics, Tome 34 (1982) no. 6, pp. 1251-1254

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1. Introduction. An incomplete latin rectangle on t symbols σ1 ..., σt of size r × s is an r × s matrix in which each cell is occupied by exactly one of the symbols σ1 ..., σt in such a way that no symbol occurs more than once in any row or more than once in any column. If r = t or s = t then it is a latin rectangle; if r = s < t it is an incomplete latin square; if r = s = t it is a latin square. The diagonal of a latin square consists of the cells (i, i) (1 ≦ i ≦ t) together with the symbols occupying those cells. Let an allowed sequence of length t be a sequence of length t in which no symbol occurs exactly t – 1 times. Let an allowed diagonal of length t be a diagonal occupied by an allowed sequence. 
Hilton, A. J. W.; Rodger, C. A. Latin Squares with Prescribed Diagonals. Canadian journal of mathematics, Tome 34 (1982) no. 6, pp. 1251-1254. doi: 10.4153/CJM-1982-087-7
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