TP2 = Bruhat
It is shown that the Bruhat partial order on permutations is equivalent to a certain natural partial order induced by TP2 matrices and that a positive matrix is TP2 if (and only if) it satisfies certain inequalities induced by Bruhat order. (c) 2010 Elsevier B.V. All rights reserved.
Johnson, C. R. and Nasserasr, S., TP2 = Bruhat (2010). Discrete Mathematics, 310(11-Oct), 1627-1628.