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 |
|---|---|
| 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
Cite this
Best, D., Hendrey, K., Wanless, I. M., Wilson, T. E., & Wood, D. R. (2018). Transversals in Latin Arrays with Many Distinct Symbols. Journal of Combinatorial Designs, 26(2), 84-96. https://doi.org/10.1002/jcd.21566