Abstract
The weight of a partition is the sum of its nonzero coordinates. Let R and S be partitions of the same weight and be the class of all -matrices with row sums R and column sums S. For a positive integer t, the t-term rank of a matrix , denoted , is defined as the largest number of 1's in A with at most one 1 in each column and at most t 1's in each row. The term rank partition of A is the partition where . Let θ be a partition of weight equal to the number of nonzero coordinates of S. In this paper, we study conditions for the existence of a matrix with
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