Geodesic
A uniqueness result for $3$-homogeneous latin trades
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 2, pp. 337-358 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

A latin trade is a subset of a latin square which may be replaced with a disjoint mate to obtain a new latin square. A $k$-homogeneous latin trade is one which intersects each row, each column and each entry of the latin square either $0$ or $k$ times. In this paper, we show that a construction given by Cavenagh, Donovan and Drápal for $3$-homogeneous latin trades in fact classifies every minimal $3$-homogeneous latin trade. We in turn classify all $3$-homogeneous latin trades. A corollary is that any $3$-homogeneous latin trade may be partitioned into three, disjoint, partial transversals.
A latin trade is a subset of a latin square which may be replaced with a disjoint mate to obtain a new latin square. A $k$-homogeneous latin trade is one which intersects each row, each column and each entry of the latin square either $0$ or $k$ times. In this paper, we show that a construction given by Cavenagh, Donovan and Drápal for $3$-homogeneous latin trades in fact classifies every minimal $3$-homogeneous latin trade. We in turn classify all $3$-homogeneous latin trades. A corollary is that any $3$-homogeneous latin trade may be partitioned into three, disjoint, partial transversals.
Classification : 05B15
Keywords: latin square; latin trade; critical set 
@article{CMUC_2006_47_2_a10,
     author = {Cavenagh, Nicholas J.},
     title = {A uniqueness result for $3$-homogeneous latin trades},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {337--358},
     year = {2006},
     volume = {47},
     number = {2},
     mrnumber = {2241536},
     zbl = {1138.05007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2006_47_2_a10/}
}
TY  - JOUR
AU  - Cavenagh, Nicholas J.
TI  - A uniqueness result for $3$-homogeneous latin trades
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2006
SP  - 337
EP  - 358
VL  - 47
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMUC_2006_47_2_a10/
LA  - en
ID  - CMUC_2006_47_2_a10
ER  - 
%0 Journal Article
%A Cavenagh, Nicholas J.
%T A uniqueness result for $3$-homogeneous latin trades
%J Commentationes Mathematicae Universitatis Carolinae
%D 2006
%P 337-358
%V 47
%N 2
%U http://geodesic.mathdoc.fr/item/CMUC_2006_47_2_a10/
%G en
%F CMUC_2006_47_2_a10
Cavenagh, Nicholas J. A uniqueness result for $3$-homogeneous latin trades. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 2, pp. 337-358. http://geodesic.mathdoc.fr/item/CMUC_2006_47_2_a10/