Geodesic
MAXIMUM GENUS EMBEDDINGS OF LATIN SQUARES
Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 495-504

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DOI

It is proved that every non-trivial Latin square has an upper embedding in a non-orientable surface and every Latin square of odd order has an upper embedding in an orientable surface. In the latter case, detailed results about the possible automorphisms and their actions are also obtained. 
GRIGGS, TERRY S.; PSOMAS, CONSTANTINOS; ŠIRÁŇ, JOZEF. MAXIMUM GENUS EMBEDDINGS OF LATIN SQUARES. Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 495-504. doi: 10.1017/S0017089517000234
@article{10_1017_S0017089517000234,
     author = {GRIGGS, TERRY S. and PSOMAS, CONSTANTINOS and \v{S}IR\'A\v{N}, JOZEF},
     title = {MAXIMUM {GENUS} {EMBEDDINGS} {OF} {LATIN} {SQUARES}},
     journal = {Glasgow mathematical journal},
     pages = {495--504},
     year = {2018},
     volume = {60},
     number = {2},
     doi = {10.1017/S0017089517000234},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000234/}
}
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