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Matrices in A(R,S) with minimum t-term ranks
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Orientador(es)
Resumo(s)
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.
Descrição
Fundacao para a Ciencia e a Tecnologia through the projects UID/MAT/00297/2019 and UID/MAT/00212/2019.
Palavras-chave
(0,1)-matrix Gale-Ryser Theorem Network flows t-term rank Algebra and Number Theory Numerical Analysis Geometry and Topology Discrete Mathematics and Combinatorics