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arXiv · 1011.5870

On the t-Term Rank of a Matrix

Richard A. Brualdi·Kathleen P. Kiernan·Seth A. Meyer·Michael W. Schroeder
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Abstract

For t a positive integer, the t-term rank of a (0,1)-matrix A is defined to be the largest number of 1s in A with at most one 1 in each column and at most t 1s in each row. Thus the 1-term rank is the ordinary term rank. We generalize some basic results for the term rank to the t-term rank, including a formula for the maximum term rank over a nonempty class of (0,1)-matrices with the the same row sum and column sum vectors. We also show the surprising result that in such a class there exists a matrix which realizes all of the maximum terms ranks between 1 and t.

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Richard A. Brualdi, Kathleen P. Kiernan, Seth A. Meyer, Michael W. Schroeder. 2010-11-26. On the t-Term Rank of a Matrix. https://arxiv.org/abs/1011.5870

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