Partial Latin Squares Are Avoidable
A square array is avoidable if for each set of n symbols there is an n × n Latin square on these symbols which differs from the array in every cell. The main result of this paper is that for m ≥ 2 any partial Latin square of order 4 m − 1 is avoidable, thus concluding the proof that any partial Lati...
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| Veröffentlicht in: | Annals of combinatorics 2011-09, Vol.15 (3), p.485-497 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | A square array is
avoidable
if for each set of
n
symbols there is an
n
×
n
Latin square on these symbols which differs from the array in every cell. The main result of this paper is that for
m
≥ 2 any partial Latin square of order 4
m
− 1 is avoidable, thus concluding the proof that any partial Latin square of order at least 4 is avoidable. |
|---|---|
| ISSN: | 0218-0006 0219-3094 0219-3094 |
| DOI: | 10.1007/s00026-011-0106-5 |