Conditions to Extend Partial Latin Rectangles

Details Conditions to Extend Partial Latin Rectangles Conditions to Extend Partial Latin Rectangles

2011-08-09

arxiv.org/abs/1108.1913v1

Mathematics

Combinatorics

15 pages

Scientific paper

In 1974 Allan Cruse provided necessary and sufficient conditions to extend an
$r\times s$ partial latin rectangle consisting of $t$ distinct symbols to a
latin square of order $n$. Here we provide some generalizations and
consequences of this result. Our results are obtained via an alternative proof
of Cruse's theorem.

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