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On the t-Term Rank of a Matrix | Richard A. Brualdi
; Kathleen P. Kiernan
; Seth A. Meyer
; Michael W. Schroeder
; | Date: |
26 Nov 2010 | 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. | Source: | arXiv, 1011.5870 | Services: | Forum | Review | PDF | Favorites |
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