TY - JOUR

T1 - Minimal matrices in the Bruhat order for symmetric (0, 1)-matrices

AU - Fernandes, Maria do Rosário Silva Franco

AU - Furtado, Susana

AU - F. da Cruz, Henrique

N1 - sem pdf conforme despacho.
Fundaçãopara a Ciencia e a Tecnologia - (UID/MAT/00212/2013; UID/MAT/00297/2013; UID/MAT/04721/2013)

PY - 2017

Y1 - 2017

N2 - In this paper we study the minimal matrices for the Bruhat order on the class of symmetric (0, 1)-matrices with given row sum vector. We will show that, when restricted to the symmetric matrices, new minimal matrices may appear besides the symmetric matrices for the nonrestricted Bruhat order. We modify the algorithm presented by Brualdi and Hwang (2004), which gives a minimal matrix for the Bruhat order on the class of (0, 1)-matrices with given row and column sum vectors, in order to obtain a minimal matrix for the Bruhat order on the class of symmetric (0, 1)-matrices with given row sum vector. We identify other minimal matrices in some of these classes. Namely, we determine all the minimal matrices when the row sums are constant and equal to 3. We then describe a family of symmetric matrices that are minimal for the Bruhat order on the class of 2k-by-2k (0, 1)-matrices with constant row sums equal to k + 1 and identify, in terms of the term rank of a matrix, a class of symmetric matrices that are related in the Bruhat order with one of these minimal matrices. (C) 2017 Elsevier Inc. All rights reserved.

AB - In this paper we study the minimal matrices for the Bruhat order on the class of symmetric (0, 1)-matrices with given row sum vector. We will show that, when restricted to the symmetric matrices, new minimal matrices may appear besides the symmetric matrices for the nonrestricted Bruhat order. We modify the algorithm presented by Brualdi and Hwang (2004), which gives a minimal matrix for the Bruhat order on the class of (0, 1)-matrices with given row and column sum vectors, in order to obtain a minimal matrix for the Bruhat order on the class of symmetric (0, 1)-matrices with given row sum vector. We identify other minimal matrices in some of these classes. Namely, we determine all the minimal matrices when the row sums are constant and equal to 3. We then describe a family of symmetric matrices that are minimal for the Bruhat order on the class of 2k-by-2k (0, 1)-matrices with constant row sums equal to k + 1 and identify, in terms of the term rank of a matrix, a class of symmetric matrices that are related in the Bruhat order with one of these minimal matrices. (C) 2017 Elsevier Inc. All rights reserved.

KW - (0 , 1)-matrices

KW - Bruhat order

KW - Minimal matrices

KW - Symmetric matrices

KW - Term rank

U2 - 10.1016/j.laa.2017.05.014

DO - 10.1016/j.laa.2017.05.014

M3 - Article

VL - 530

SP - 160

EP - 184

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -