TY - JOUR
T1 - Classes of (0,1)-matrices Where the Bruhat Order and the Secondary Bruhat Order Coincide
AU - Fernandes, Rosário
AU - da Cruz, Henrique F.
AU - Salomão, Domingos
N1 - FCT (UID/MAT/00212/2019)
FCT (UID/MAT/00297/2019)
PY - 2020/7/1
Y1 - 2020/7/1
N2 - Given two nonincreasing integral vectors R and S, with the same sum, we denote by A(R, S) the class of all (0,1)-matrices with row sum vector R, and column sum vector S. The Bruhat order and the Secondary Bruhat order on A(R, S) are both extensions of the classical Bruhat order on Sn, the symmetric group of degree n. These two partial orders on A(R, S) are, in general, different. In this paper we prove that if R = (2,2,…,2) or R = (1,1,…,1), then the Bruhat order and the Secondary Bruhat order on A(R, S) coincide.
AB - Given two nonincreasing integral vectors R and S, with the same sum, we denote by A(R, S) the class of all (0,1)-matrices with row sum vector R, and column sum vector S. The Bruhat order and the Secondary Bruhat order on A(R, S) are both extensions of the classical Bruhat order on Sn, the symmetric group of degree n. These two partial orders on A(R, S) are, in general, different. In this paper we prove that if R = (2,2,…,2) or R = (1,1,…,1), then the Bruhat order and the Secondary Bruhat order on A(R, S) coincide.
KW - (0,1)-matrices
KW - Bruhat order
KW - Partial order
KW - Secondary Bruhat order
UR - http://www.scopus.com/inward/record.url?scp=85068123460&partnerID=8YFLogxK
U2 - 10.1007/s11083-019-09500-8
DO - 10.1007/s11083-019-09500-8
M3 - Article
AN - SCOPUS:85068123460
VL - 37
SP - 207
EP - 221
JO - Order-A Journal On The Theory Of Ordered Sets And Its Applications
JF - Order-A Journal On The Theory Of Ordered Sets And Its Applications
SN - 0167-8094
IS - 2
ER -