Minimal homogeneous latin trades

Minimal homogeneous latin trades

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 d-homogeneous latin trade is one which intersects each row, each column and each entry of the latin square either 0 or d times. In this paper we give a construction for minimal d-homogeneous latin trades of size dm, for every integer d 3, and m 1.75d2 + 3. We also improve this b...

4-homogeneous Latin Trades

3-Homogeneous latin trades

The Spectrum for 3-Way k-Homogeneous Latin Trades

A μ-way k-homogeneous Latin trade was defined by Bagheri Gh, Donovan, Mahmoodian (2012), where the existence of 3-way k-homogeneous Latin trades was specifically investigated. We investigate the existence of a certain class of μ-way k-homogeneous Latin trades with an idempotent like property. We present a number of constructions for μ-way k-homogeneous Latin trades with this property, and show ...

Biembeddings of symmetric configurations and 3-homogeneous Latin trades

Using results of Altshuler and Negami, we present a classification of biembeddings of symmetric configurations of triples in the torus or Klein bottle. We also give an alternative proof of the structure of 3-homogeneous