Minimal 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...

On the intersection of three or four transversals of the back circulant latin squares

Cavenagh and Wanless [Discrete Appl. Math. 158 no. 2 (2010), 136–146] determined the possible intersection of any two transversals of the back circulant latin square Bn, and used the result to completely determine the spectrum for 2-way k-homogeneous latin trades. We generalize this problem to the intersection of μ transversals of Bn such that the transversals intersect stably (that is, the int...

4-homogeneous Latin Trades

3-Homogeneous latin trades