Latin squares and their defining sets
| dc.creator | Meszaros, Karola | |
| dc.date | 2005-09-19 | |
| dc.date.accessioned | 2026-07-07T06:18:10Z | |
| dc.date.available | 2026-07-07T06:18:10Z | |
| dc.description | A Latin square $L(n,k)$ is a square of order $n$ with its entries colored with $k$ colors so that all the entries in a row or column have different colors. Let $d(L(n,k))$ be the minimal number of colored entries of an $n \times n$ square such that there is a unique way of coloring of the yet uncolored entries in order to obtain a Latin square $L(n, k)$. In this paper we discuss the properties of $d(L(n,k))$ for $k=2n-1$ and $k=2n-2$. We give an alternate proof of the identity $d(L(n, 2n-1))=n^2-n$, which holds for even $n$, and we establish the new result $d(L(n, 2n-2)) \geq n^2-\lfloor\frac{8n}{5}\rfloor$ and show that this bound is tight for $n$ divisible by 10. | |
| dc.description | 16 pages, 24 figures | |
| dc.identifier | https://arxiv.org/abs/math/0509410 | |
| dc.identifier | http://arxiv.org/abs/math/0509410 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94645 | |
| dc.subject | Combinatorics | |
| dc.subject | 05B15 | |
| dc.title | Latin squares and their defining sets | |
| dc.type | text |