On the term rank partition

For each positive integer t, the t-term rank of a (0,1)-matrix A is 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 [5] R. Brualdi et al. (2012) stated several results for the t-term rank, including a formula for the maximum t-term rank over a nonempty class of (0,1)-matrices with the same row sum and column sum vectors. In this paper we state more results for the t-term rank. Using these results we define and we study the term rank partition. We also deduce a formula for the minimal t-term rank over a nonempty class of (0,1)-matrices with the same row sum and column sum vectors.