Indivisible plexes in latin squares

Bryant, D., Egan, J., Maenhaut, B. and Wanless, I. M. (2009) Indivisible plexes in latin squares. Designs, Codes and Cryptography, 52 1: 93-105. doi:10.1007/s10623-009-9269-z

Author Bryant, D.
Egan, J.
Maenhaut, B.
Wanless, I. M.
Title Indivisible plexes in latin squares
Journal name Designs, Codes and Cryptography   Check publisher's open access policy
ISSN 0925-1022
Publication date 2009-07-01
Sub-type Article (original research)
DOI 10.1007/s10623-009-9269-z
Volume 52
Issue 1
Start page 93
End page 105
Total pages 13
Editor D. Jungnickel
J. D. Key
P. Wild
Place of publication United States
Publisher Springer
Language eng
Subject C1
970101 Expanding Knowledge in the Mathematical Sciences
010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)
Formatted abstract
A k-plex is a selection of kn entries of a latin square of order n in which each row, column and symbol is represented precisely k times. A transversal of a latin square corresponds to the case k = 1. A k-plex is said to be indivisible if it contains no c-plex for any 0 < c < k. We prove that if n = 2km for integers k ≥ 2 and m ≥ 1 then there exists a latin square of order n composed of 2m disjoint indivisible k-plexes. Also, for positive integers k and n satisfying n = 3k, n = 4k or n ≥ 5k, we construct a latin square of order n containing an indivisible k-plex.
Keyword Latin square
Orthogonal partition
Q-Index Code C1
Q-Index Status Confirmed Code

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2010 Higher Education Research Data Collection
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Citation counts: TR Web of Science Citation Count  Cited 12 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 13 times in Scopus Article | Citations
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Created: Sat, 22 Aug 2009, 01:56:22 EST by Marie Grove on behalf of School of Mathematics & Physics