The Spectrum for $3$-Way $k$-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 ...

On the existence of 3-way k-homogeneous Latin trades

A μ-way Latin trade of volume s is a collection of μ partial Latin squares T1, T2, . . . , Tμ, containing exactly the same s filled cells, such that if cell (i, j) is filled, it contains a different entry in each of the μ partial Latin squares, and such that row i in each of the μ partial Latin squares contains, set-wise, the same symbols and column j, likewise. It is called μ–way k–homogeneous...

3-Homogeneous latin trades

4-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...