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A  gerechte framework  is a partition of an  n  ×  n  array into  n  regions of  n  cells each. A  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  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 toward 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  ×  t  rectangle or a  t  ×  s  rectangle is realizable. © 2011 Wiley Periodicals, Inc. J Combin Designs 20:112‐123, 2012

Gerechte designs with rectangular regions