Occupancy of a rectangular array

Open Access
Publisher Website
Google Scholar
Abstract
The problem addressed is: the occupancy, by non-negative integers, of a rectangular array of given size when the row sums and column sums are all fixed. In general, a single expression for the number of array element combinations which covers all combinations of row and column sums cannot be found. Thus two algorithms which systematically count all element combinations are presented, the first applying to arrays with only two columns and the second to arrays with any number of rows and columns. The two-column algorithm is then used to derive expressions for the number of array element combinations of arrays having three rows and two columns. Five different expressions are required to cover all combinations of row and column totals.

This publication has 0 references indexed in Scilit: