- LINEAR TRANSFORMATIONS THAT PRESERVE THE ASSIGNMENT II
- Leroy B.Beasley ; Lee, Gwang-Yeon ; Lee, Sang-Gu ;
- Journal of the Korean Mathematical Society, volume 33, issue 3, 1996, Pages 527~539
Abstract
Let $R = (r_1, r_2, \cdots, r_m) and S = (s_1, s_2, \cdots, s_n)$ be vectors of positive integers, and let $U(R,S)$ denote the class of all $m \times n$ matrices $A = [a_{ij}]$ of 0's and 1's such that $$ \sum_{k = 1}^{n} a_{ik} = r_i (i = 1, 2, \cdots, m), $$ $$ \sum_{k = 1}^{m} a_{kj} = s_j (j = 1, 2, \cdots, n). $$