Magic rectangles revisited

AbstractMagic rectangles are a generalization of magic squares that have been recently investigated by Bier and Rogers (European J. Combin. 14 (1993) 285–299); and Bier and Kleinschmidt (Discrete Math. 176 (1997) 29–42). In this paper, we present a new, simplified proof of the necessary and sufficient conditions for a magic rectangle to exist. We also show that magic rectangles, under the natural multiplication, have a unique factorization as a product of irreducible magic rectangles

Generalized Semimagic Squares for Digital Halftoning

Completing Aronov et al.'s study on zero-discrepancy matrices for digital halftoning, we determine all (m, n, k, l) for which it is possible to put mn consecutive integers on an m-by-n board (with wrap-around) so that each k-by-l region holds the same sum. For one of the cases where this is impossible, we give a heuristic method to find a matrix with small discrepancy.Comment: 6 pages, 6 figure