On completing three cyclically generated transversals to a latin square

Cavenagh, Nicholas J., Hamalainen, Carlo and Nelson, Adrian M. (2009) On completing three cyclically generated transversals to a latin square. Finite Fields and Their Applications, 15 3: 294-303. doi:10.1016/j.ffa.2008.05.009


Author Cavenagh, Nicholas J.
Hamalainen, Carlo
Nelson, Adrian M.
Title On completing three cyclically generated transversals to a latin square
Journal name Finite Fields and Their Applications   Check publisher's open access policy
ISSN 1071-5797
1090-2465
Publication date 2009-06
Sub-type Article (original research)
DOI 10.1016/j.ffa.2008.05.009
Volume 15
Issue 3
Start page 294
End page 303
Total pages 10
Place of publication Maryland Heights, MO, United States
Publisher Academic Press
Language eng
Formatted abstract
Let P be a partial latin square of prime order p > 7 consisting of three cyclically generated transversals. Specifically, let P be a partial latin square of the form:

P = {(i, c + i, s + i), (i, c′ + i, s′ + i), (i, c″ + i, s″ + i) | 0 ≤ i < p}

for some distinct c, c′, c″ and some distinct s, s′, s″. In this paper we show that any such P completes to a latin square which is diagonally cyclic. Equivalently, we prove that for each prime p > 7, every partial transversal of size 3 in the addition table for the integers modulo p can be completed to a full transversal.
Keyword Latin square
Diagonally cyclic latin square
Transversal
Complete mapping
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Thu, 03 Sep 2009, 08:11:49 EST by Mr Andrew Martlew on behalf of Mathematics