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 -