Embedding 3 -homogeneous latin trades into abelian 2 -groups

Nicholas J. Cavenagh

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 2, page 191-212
  • ISSN: 0010-2628

Abstract

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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 = ∅ 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 show the existence of 3 -homogeneous latin trades in abelian 2 -groups.

How to cite

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Cavenagh, Nicholas J.. "Embedding $3$-homogeneous latin trades into abelian $2$-groups." Commentationes Mathematicae Universitatis Carolinae 45.2 (2004): 191-212. <http://eudml.org/doc/249361>.

@article{Cavenagh2004,
abstract = {Let $T$ be a partial latin square and $L$ be a latin square with $T\subseteq L$. We say that $T$ is a latin trade if there exists a partial latin square $T^\{\prime \}$ with $T^\{\prime \}\cap T=\emptyset $ such that $(L\setminus T)\cup T^\{\prime \}$ 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 show the existence of $3$-homogeneous latin trades in abelian $2$-groups.},
author = {Cavenagh, Nicholas J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {latin square; latin trade; abelian $2$-group; Latin square; Latin trade; abelian 2-group},
language = {eng},
number = {2},
pages = {191-212},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Embedding $3$-homogeneous latin trades into abelian $2$-groups},
url = {http://eudml.org/doc/249361},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Cavenagh, Nicholas J.
TI - Embedding $3$-homogeneous latin trades into abelian $2$-groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 2
SP - 191
EP - 212
AB - Let $T$ be a partial latin square and $L$ be a latin square with $T\subseteq L$. We say that $T$ is a latin trade if there exists a partial latin square $T^{\prime }$ with $T^{\prime }\cap T=\emptyset $ such that $(L\setminus T)\cup T^{\prime }$ 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 show the existence of $3$-homogeneous latin trades in abelian $2$-groups.
LA - eng
KW - latin square; latin trade; abelian $2$-group; Latin square; Latin trade; abelian 2-group
UR - http://eudml.org/doc/249361
ER -

References

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