On the existence of 3-way k-homogeneous Latin trades

Gh, Behrooz Bagheri, Donovan, Diane and Mahmoodian, E. S. (2012) On the existence of 3-way k-homogeneous Latin trades. Discrete Mathematics, 312 24: 3473-3481. doi:10.1016/j.disc.2012.08.020

Author Gh, Behrooz Bagheri
Donovan, Diane
Mahmoodian, E. S.
Title On the existence of 3-way k-homogeneous Latin trades
Formatted title
On the existence of 3-way k-homogeneous Latin trades
Journal name Discrete Mathematics   Check publisher's open access policy
ISSN 0012-365X
Publication date 2012-12
Sub-type Article (original research)
DOI 10.1016/j.disc.2012.08.020
Volume 312
Issue 24
Start page 3473
End page 3481
Total pages 9
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Collection year 2013
Language eng
Formatted abstract
A μ-way Latin trade of volume s is a collection of μ partial Latin squares T1,T2,…,Tμ, containing exactly the same s filled cells, such that, if cell (i,j) is filled, it contains a different entry in each of the μ partial Latin squares, and such that row i in each of the μ partial Latin squares contains, set-wise, the same symbols, and column j likewise. It is called a μ-wayk-homogeneous Latin trade if, in each row and each column, Tr, for 1≤r≤μ, contains exactly k elements, and each element appears in Tr exactly k times. It is also denoted as a (μ,k,m) Latin trade, where m is the size of the partial Latin squares.

     We introduce some general constructions for μ-way k-homogeneous Latin trades, and specifically show that, for all k≤m, 6≤k≤13, and k=15, and for all k≤m, k = 4,5 (except for four specific values), a 3-way k-homogeneous Latin trade of volume km exists. We also show that there is no (3,4,6) Latin trade and there is no (3,4,7) Latin trade. Finally, we present general results on the existence of 3-way k-homogeneous Latin trades for some modulo classes of m.
Keyword Latin square
Latin trade
μ-way Latin trade
μ-way k-homogeneous Latin trade
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2013 Collection
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Created: Sun, 16 Dec 2012, 00:52:30 EST by System User on behalf of Mathematics