Name
Abstract | ||
|---|---|---|
The full n-Latin square is the $$n\\times n$$n×n array with symbols $$1,2,\\dots ,n$$1,2,¿,n in each cell. In a way that is analogous to critical sets of full designs, a critical set of the full n-Latin square can be used to find a defining set for any Latin square of order n. In this paper we study the size of the smallest critical set for a full n-Latin square, showing this to be somewhere between $$(n^3-2n^2+2n)/2$$(n3-2n2+2n)/2 and $$(n-1)^3+1$$(n-1)3+1. In the case that each cell is either full or empty, we show the size of a critical set in the full n-Latin square is always equal to $$n^3-2n^2-n$$n3-2n2-n. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s00373-015-1590-x | Graphs and Combinatorics |
Keywords | Field | DocType |
Full Latin square, Latin square, Defining set, Critical set, O5B15 | Discrete mathematics,Square number,Combinatorics,Latin square,Unit square,Mathematics | Journal |
Volume | Issue | ISSN |
32 | 2 | 1435-5914 |
Citations | PageRank | References |
0 | 0.34 | 10 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nicholas J. Cavenagh | 1 | 92 | 20.89 |
| vaipuna raass | 2 | 0 | 0.34 |