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In a previous paper, the authors introduced and studied the Bruhat order in the class of Latin squares of order n. In this paper, we investigate the restriction of the Bruhat order in a class of isotopic Latin squares. We present equivalent conditions for two Latin squares be related by the Bruhat order when one of them is obtained from the other by interchanging rows or columns or symbols. The cover relation is also addressed, and we present orthogonal isotopic Latin squares related by the Bruhat order.
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Rosário Fernandes, Henrique F. da Cruz, Domingos Salomão, The Bruhat order on classes of isotopic Latin squares. Port. Math. 77 (2020), no. 1, pp. 111–131DOI 10.4171/PM/2046