Projects per year
Abstract
An array is row-Latin if no symbol is repeated within any row. An array is Latin if it and its transpose are both row-Latin. A transversal in an n×n array is a selection of n different symbols from different rows and different columns. We prove that every n×n Latin array containing at least (2-2)n2 distinct symbols has a transversal. Also, every n×n row-Latin array containing at least 14(5-5)n2 distinct symbols has a transversal. Finally, we show by computation that every Latin array of order 7 has a transversal, and we describe all smaller Latin arrays that have no transversal.
Original language | English |
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Pages (from-to) | 84-96 |
Number of pages | 13 |
Journal | Journal of Combinatorial Designs |
Volume | 26 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2018 |
Keywords
- Latin array
- Latin square
- Row-Latin
- Transversal
Projects
- 2 Finished
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Matchings in Combinatorial Structures
Wanless, I., Bryant, D. & Horsley, D.
Australian Research Council (ARC), Monash University, University of Queensland , University of Melbourne
1/01/15 → 10/10/20
Project: Research
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Graph colouring via entropy compression
Australian Research Council (ARC)
2/01/14 → 31/12/17
Project: Research