Subsquare-free Latin squares of odd order

Maenhaut, Barbara; Wanless, Ian M. and Webb, Bridget S. (2007). Subsquare-free Latin squares of odd order. European Journal of Combinatorics, 28(1) pp. 322–336.

DOI: https://doi.org/10.1016/j.ejc.2005.07.002

Abstract

For every odd positive integer m we prove the existence
of a Latin square of order 3m having no proper Latin subsquares. Combining this with previously known results it follows that subsquare-free Latin squares exist for all odd orders.

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