Nearly magic rectangles

Feng Shun Chai, Rakhi Singh, John Stufken

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)562-567
Number of pages6
JournalJournal of Combinatorial Designs
Volume27
Issue number9
DOIs
StatePublished - Sep 1 2019

Fingerprint

Rectangle
Magic square
Odd
Statistics
Necessary Conditions
Sufficient Conditions
Combinatorics
Generalise
Experiment

Keywords

  • magic rectangle
  • magic square
  • row-column design

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Chai, F. S., Singh, R., & Stufken, J. (2019). Nearly magic rectangles. Journal of Combinatorial Designs, 27(9), 562-567. https://doi.org/10.1002/jcd.21667

Nearly magic rectangles. / Chai, Feng Shun; Singh, Rakhi; Stufken, John.

In: Journal of Combinatorial Designs, Vol. 27, No. 9, 01.09.2019, p. 562-567.

Research output: Contribution to journalArticle

Chai, FS, Singh, R & Stufken, J 2019, 'Nearly magic rectangles', Journal of Combinatorial Designs, vol. 27, no. 9, pp. 562-567. https://doi.org/10.1002/jcd.21667
Chai FS, Singh R, Stufken J. Nearly magic rectangles. Journal of Combinatorial Designs. 2019 Sep 1;27(9):562-567. https://doi.org/10.1002/jcd.21667
Chai, Feng Shun ; Singh, Rakhi ; Stufken, John. / Nearly magic rectangles. In: Journal of Combinatorial Designs. 2019 ; Vol. 27, No. 9. pp. 562-567.
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