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Journal article
Some partial Latin cubes and their completions
European Journal of Combinatorics, Vol.32, pp.1345-1352
32
2011
Web of Science ID: WOS:000295436000016
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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Details
- Title
- Some partial Latin cubes and their completions
- Publication Details
- European Journal of Combinatorics, Vol.32, pp.1345-1352
- Resource Type
- Journal article
- Publisher
- Academic Press; United Kingdom
- Series
- 32
- Copyright
- © 2011 Elsevier Ltd. All rights reserved.
- Identifiers
- WOS:000295436000016; 99380090300806600
- Academic Unit
- Mathematics and Statistics; Hal Marcus College of Science and Engineering
- Language
- English