Conditions to Extend Partial Latin Rectangles

2011/08/09 by Serge C. Ballif, Ballif, Serge C.
Computer Science · Engineering · Mathematics · #Mathematics and Applications #graph theory and CDMA systems #math.CO #msc:05B15 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1108.1913

15 pages

arxiv created 2011/08/09 · arxiv updated 2011/08/10

Abstract

In 1974 Allan Cruse provided necessary and sufficient conditions to extend an r× 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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