A uniqueness result for $3$-homogeneous latin trades

Cavenagh, Nicholas J.. "A uniqueness result for $3$-homogeneous latin trades." Commentationes Mathematicae Universitatis Carolinae 47.2 (2006): 337-358. <http://eudml.org/doc/249888>.

@article{Cavenagh2006,
abstract = {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.},
author = {Cavenagh, Nicholas J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {latin square; latin trade; critical set; Latin square; Latin trade; critical set; transversal},
language = {eng},
number = {2},
pages = {337-358},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A uniqueness result for $3$-homogeneous latin trades},
url = {http://eudml.org/doc/249888},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Cavenagh, Nicholas J.
TI - A uniqueness result for $3$-homogeneous latin trades
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 2
SP - 337
EP - 358
AB - 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.
LA - eng
KW - latin square; latin trade; critical set; Latin square; Latin trade; critical set; transversal
UR - http://eudml.org/doc/249888
ER -

References

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