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Counting the number of p\(\times q\) integer matrices more concordant than a given matrix. (English) Zbl 0569.15008

The author gives a characterization, an algorithm, and an enumeration formula for sets of integer matrices whose partial sum matrices (all entries to the left and above a given entry) are greater than or equal to those of a given matrix. This gives results on matrices with row, column sums specified.
Reviewer: K.H.Kim

MSC:

15B36 Matrices of integers
15B48 Positive matrices and their generalizations; cones of matrices
05A15 Exact enumeration problems, generating functions
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