Classes of (0,1 )-matrices Where the Bruhat Order and the Secondary Bruhat Order Coincide

摘要

Given two nonincreasing integral vectorsRandS, with the same sum, we denote byA(R,S)documentclass the class of all (0,1)-matrices with row sum vectorR, and column sum vectorS. The Bruhat order and the Secondary Bruhat order onA(R,S)documentclass are both extensions of the classical Bruhat order onS(n), the symmetric group of degreen. These two partial orders onA(R,S)documentclass are, in general, different. In this paper we prove that ifR= (2,2, horizontal ellipsis ,2) orR= (1,1, horizontal ellipsis ,1), then the Bruhat order and the Secondary Bruhat order onA(R,S)documentclass coincide.