Gerechte Designs with Rectangular Regions
  A \emph{gerechte framework} is a partition of an $n \times n$ array into $n$ regions of $n$ cells each. A \emph{realization} of a gerechte framework is a latin square of order $n$ with the property that when its cells are partitioned by the framework, each region contains exactly one copy of each symbol. A \emph{gerechte design} is a gerechte framework together with a realization.   We investigate gerechte frameworks where each region is a rectangle. It seems plausible that all such frameworks have realizations, and we present some progress towards answering this question. In particular, we show that for all positive integers $s$ and $t$, any gerechte framework where each region is either an $s \times t$ rectangle or a $t\times s$ rectangle is realizable. 
J. Courtiel and E. R. Vaughan
math.CO