article

3-Homogeneous latin trades

Authors:

Nicholas Cavenagh,

Aleš DrápalAuthors Info & Claims

Discrete Mathematics, Volume 300, Issue 1-3

Pages 57 - 70

https://doi.org/10.1016/j.disc.2005.04.021

Published: 01 September 2005 Publication History

Abstract

Let T be a partial latin square and L be a latin square with T@?L. We say that T is a latin trade if there exists a partial latin square T^' with T^'@?T=@A such that (L@?T)@?T^' is a latin square. A k-homogeneous latin trade is one which intersects each row, each column and each entry either 0 or k times. In this paper, we construct 3-homogeneous latin trades from hexagonal packings of the plane with circles. We show that 3-homogeneous latin trades of size 3m exist for each m>=3. This paper discusses existence results for latin trades and provides a glueing construction which is subsequently used to construct all latin trades of finite order greater than three.

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Cited By

Bagheri Gh. BDonovan DMahmoodian E(2012)On the existence of 3 -way k -homogeneous Latin tradesDiscrete Mathematics10.1016/j.disc.2012.08.020312:24(3473-3481)Online publication date: 28-Dec-2012
https://dl.acm.org/doi/10.1016/j.disc.2012.08.020
Cavenagh NWanless I(2010)On the number of transversals in Cayley tables of cyclic groupsDiscrete Applied Mathematics10.1016/j.dam.2009.09.006158:2(136-146)Online publication date: 1-Jan-2010
https://dl.acm.org/doi/10.1016/j.dam.2009.09.006
Lefevre JDonovan DDrápal A(2008)Permutation Representation of 3 and 4-Homogenous Latin BitradesFundamenta Informaticae10.5555/2365293.236530184:1(99-110)Online publication date: 1-Jan-2008
https://dl.acm.org/doi/10.5555/2365293.2365301
Show More Cited By

Index Terms

3-Homogeneous latin trades
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms

Index terms have been assigned to the content through auto-classification.

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Copyright © © 2005.

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Elsevier Science Publishers B. V.

Netherlands

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Published: 01 September 2005

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Cited By

Bagheri Gh. BDonovan DMahmoodian E(2012)On the existence of 3 -way k -homogeneous Latin tradesDiscrete Mathematics10.1016/j.disc.2012.08.020312:24(3473-3481)Online publication date: 28-Dec-2012
https://dl.acm.org/doi/10.1016/j.disc.2012.08.020
Cavenagh NWanless I(2010)On the number of transversals in Cayley tables of cyclic groupsDiscrete Applied Mathematics10.1016/j.dam.2009.09.006158:2(136-146)Online publication date: 1-Jan-2010
https://dl.acm.org/doi/10.1016/j.dam.2009.09.006
Lefevre JDonovan DDrápal A(2008)Permutation Representation of 3 and 4-Homogenous Latin BitradesFundamenta Informaticae10.5555/2365293.236530184:1(99-110)Online publication date: 1-Jan-2008
https://dl.acm.org/doi/10.5555/2365293.2365301
Lefevre JDonovan DDrápal A(2008)Permutation Representation of 3 and 4-Homogenous Latin BitradesFundamenta Informaticae10.5555/1402623.140263184:1(99-110)Online publication date: 1-Jan-2008
https://dl.acm.org/doi/10.5555/1402623.1402631
Cavenagh NDrápal AHämäläinen C(2008)Latin bitrades derived from groupsDiscrete Mathematics10.1016/j.disc.2007.11.041308:24(6189-6202)Online publication date: 1-Dec-2008
https://dl.acm.org/doi/10.1016/j.disc.2007.11.041

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