The Bruhat order on classes of isotopic Latin squares

Abstract

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.

On the little secondary Bruhat order

“…Doing this they gave rise to two distinct partial order relations on A(R, S). In the last 16 years, many research have focused on several topics of these two partial order relations: conjectures [15], minimal elements [2,4,16], coincidence [12], chains and antichains [9,10,20,21], restrictions of the Bruhat order on subclasses of A(R, S) [8,11], or extensions of one of these orders to other classes of matrices distinct of A(R, S) [5,6,7,13,14].…”