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 -