an:07141832
Zbl 1428.05041
Chai, Feng-shun; Singh, Rakhi; Stufken, John
Nearly magic rectangles
EN
J. Comb. Des. 27, No. 9, 562-567 (2019).
00438905
2019
j
05B15
magic rectangle; magic square; row-column design
Summary: Magic squares have been extremely useful and popular in combinatorics and statistics. One generalization of magic squares is magic rectangles which are useful for designing experiments in statistics. A necessary and sufficient condition for the existence of magic rectangles restricts the number of rows and columns to be either both odd or both even. In this paper, we generalize magic rectangles to even by odd nearly magic rectangles. We also prove necessary and sufficient conditions for the existence of a nearly magic rectangle, and construct one for each parameter set for which they exist.