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Existence of self‐conjugate self‐orthogonal diagonal latin squares
Author(s) -
Bennett F. E.,
Du B.,
Zhang H.
Publication year - 1998
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1998)6:1<51::aid-jcd4>3.0.co;2-v
Subject(s) - mathematics , diagonal , latin square , combinatorics , conjecture , orthogonal array , conjugate , order (exchange) , statistics , mathematical analysis , geometry , taguchi methods , finance , economics , rumen , chemistry , food science , fermentation
In this article we give some new constructions of self‐conjugate self‐orthogonal diagonal Latin squares (SCSODLS). As an application of such constructions, we give a conclusive result regarding the existence of SCSODLS and show that there exists an SCSODLS of order n if and only if n ≡ 0, 1 (mod 4), except for n = 5. This result completely disproves a conjecture of Danhof, Phillips, and Wallis about SCSODLS in Danhof, Philips, and Wallis, JCMCC, 8 (1990), 3–8. © 1998 John Wiley & Sons, Inc. J Combin Designs 6:51–62, 1998