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Some partial Latin cubes and their completions
Journal article   Peer reviewed

Some partial Latin cubes and their completions

Jaromy Kuhl and Tristan Denley
European Journal of Combinatorics, Vol.32, pp.1345-1352
32
2011
DOI: https://doi.org/10.1016/j.ejc.2011.05.003
Web of Science ID: WOS:000295436000016

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Abstract

It is well known that all n×n partial Latin squares with at most n−1 entries are completable. Our intent is to extend this well known statement to partial Latin cubes. We show that if an n×n×n partial Latin cube contains at most n − 1 entries, no two of which occupy the same row, then the partial Latin cube is completable. Also included in this paper is the problem of completing 2×n×n partial Latin boxes with at most n − 1 entries. Given certain sufficient conditions, we show when such partial Latin boxes are completable and then extendable to a deeper Latin box.

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