TY - JOUR

T1 - Matrices in A(R,S) with minimum t-term ranks

AU - Fernandes, Rosário

AU - da Cruz, Henrique F.

AU - Palheira, Susana C.

N1 - Fundacao para a Ciencia e a Tecnologia through the projects UID/MAT/00297/2019 and UID/MAT/00212/2019.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - Let R and S be two sequences of nonnegative integers in nonincreasing order which have the same sum, and let A(R,S) be the class of all (0,1)-matrices which have row sums given by R and column sums given by S. For a positive integer t, the t-term rank of a (0,1)-matrix A is defined as the maximum number of 1's in A with at most one 1 in each column and at most t 1's in each row. In this paper, we address conditions for the existence of a matrix in A(R,S) that realizes all the minimum t-term ranks, for t≥1.

AB - Let R and S be two sequences of nonnegative integers in nonincreasing order which have the same sum, and let A(R,S) be the class of all (0,1)-matrices which have row sums given by R and column sums given by S. For a positive integer t, the t-term rank of a (0,1)-matrix A is defined as the maximum number of 1's in A with at most one 1 in each column and at most t 1's in each row. In this paper, we address conditions for the existence of a matrix in A(R,S) that realizes all the minimum t-term ranks, for t≥1.

KW - (0,1)-matrix

KW - Gale-Ryser Theorem

KW - Network flows

KW - t-term rank

UR - http://www.scopus.com/inward/record.url?scp=85074108050&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2019.10.010

DO - 10.1016/j.laa.2019.10.010

M3 - Article

AN - SCOPUS:85074108050

SN - 0024-3795

VL - 586

SP - 239

EP - 261

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -