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

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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.

Original languageEnglish
Pages (from-to)239-261
Number of pages23
JournalLinear Algebra and its Applications
Publication statusPublished - 1 Feb 2020


  • (0,1)-matrix
  • Gale-Ryser Theorem
  • Network flows
  • t-term rank


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