arXiv
Open Access
2019
Small Latin arrays have a near transversal
Darcy Best
Kyle Pula
Ian M. Wanless
Abstrak
A Latin array is a matrix of symbols in which no symbol occurs more than once within a row or within a column. A diagonal of an $n\times n$ array is a selection of $n$ cells taken from different rows and columns of the array. The weight of a diagonal is the number of different symbols on it. We show via computation that every Latin array of order $n\le11$ has a diagonal of weight at least $n-1$. A corollary is the existence of near transversals in Latin squares of these orders. More generally, for all $k\le20$ we compute a lower bound on the order of any Latin array that does not have a diagonal of weight at least $n-k$.
Topik & Kata Kunci
Penulis (3)
D
Darcy Best
K
Kyle Pula
I
Ian M. Wanless
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2019
- Bahasa
- en
- Sumber Database
- arXiv
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- Open Access ✓