A lower bound for the size of the largest critical sets in Latin squares
| dc.creator | Hatami, Hamed | |
| dc.creator | Mahmoodian, Ebadollah S. | |
| dc.date | 2006-12-31 | |
| dc.date.accessioned | 2026-07-07T07:37:56Z | |
| dc.date.available | 2026-07-07T07:37:56Z | |
| dc.description | A critical set in an $n \times n$ array is a set $C$ of given entries, such that there exists a unique extension of $C$ to an $n\times n$ Latin square and no proper subset of $C$ has this property. The cardinality of the largest critical set in any Latin square of order $n$ is denoted by $\lcs{n}$. We give a lower bound for $\lcs{n}$ by showing that $\lcs{n} \geq n^2(1-\frac{2 + \ln 2}{\ln n})+n(1+\frac {\ln (8 π)} {\ln n})-\frac{\ln 2}{\ln n}.$ | |
| dc.identifier | https://arxiv.org/abs/math/0701014 | |
| dc.identifier | http://arxiv.org/abs/math/0701014 | |
| dc.identifier | Bulletin of the Institute of Combinatorics and its Applications (Canada). 38 (2003) pp.19-22 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120950 | |
| dc.subject | Combinatorics | |
| dc.subject | 05B15 | |
| dc.title | A lower bound for the size of the largest critical sets in Latin squares | |
| dc.type | text |