Bruhat order, Permutations, TP2 matrix, Total positivity
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.
Johnson, Charles R. and Nasserasr, Shahla, "TP2=Bruhat" (2010). Mathematics Faculty Articles. 128.