Nearly magic rectangles. Issue 9 (6th July 2019)

• Record Type: Journal Article
• Authors: Chai, Feng‐Shun; Singh, Rakhi; Stufken, John
• Is Part Of: Journal of combinatorial designs. Volume 27:Issue 9(2019:Sep.)
• Page Start: 562
• Page End: 567
• Publication Date: 2019-07-06
• Subjects: magic rectangle -- magic square -- row‐column design; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21667
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: 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.