2019/12/18 by Khodkar, Abdollah, Leach, David, Ellis, Brandi
#05-02 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1912.08536
A \em signed magic rectangle SMR(m,n;k, s) is an m × n array with entries from X, where X=\0,±1,±2,…, ± (mk-1)/2\ if mk is odd and X = \±1,±2,…,± mk/2\ if mk is even, such that precisely k cells in every row and s cells in every column are filled, every integer from set X appears exactly once in the array and the sum of each row and of each column is zero. In this paper, we prove that a signed magic rectangle SMR(m,n;k, 3) exists if and only if 3≤ m,k≤ n and mk=3n.