An algorithm for finding the number of (0, 1, 2,…, l)-matrices with prefixed row sum and column sum vectors

Abstract

Let m n and k (with k n m) be positive integers and let R = (r ₁,…r _m ) and S = (s ₁,…s _n ) be two partitions of k into m and n parts, respectively. In this work we present a simple algorithm for the direct calculation of the number of m × n (0, 1)-matrices having r _i 1's in row i and s _j 1's in column j. We also extend the above procedure to the general case of (0, l, 2,…l)-matrices with prefixed row sum and column sum vectors.

Keywords:

• (0, l)-matrices
• (0, 1, 2,…,l)-matrices

C.R. Categories:

• G.2.1.