Gerechte designs with rectangular regions

✍ Scribed by J. Courtiel; E. R. Vaughan

• Book ID: 102310016
• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 152 KB
• Volume: 20
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20300

✦ Synopsis

Abstract

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