Name
Abstract | ||
|---|---|---|
In this paper we develop two methods for completing partial latin squares and prove the following. Let \(A\) be a partial latin square of order \(nr\) in which all non-empty cells occur in at most \(n-1\) \(r\times r\) squares. If \(t_1,\ldots , t_m\) are positive integers for which \(n\geqslant t_1^2+t_2^2+\cdots +t_m^2+1\) and if \(A\) is the union of \(m\) subsquares each with order \(rt_i\), then \(A\) can be completed. We additionally show that if \(n\geqslant r+1\) and \(A\) is the union of \(n\) identical \(r\times r\) squares with disjoint rows and columns, then \(A\) can be completed. For smaller values of \(n\) we show that a completion does not always exist. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s00373-015-1571-0 | Graphs and Combinatorics |
Keywords | Field | DocType |
Partial, Latin square, Completion | Integer,Row and column spaces,Combinatorics,Disjoint sets,Latin square,Mathematics | Journal |
Volume | Issue | ISSN |
32 | 1 | 1435-5914 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jaromy Kuhl | 1 | 10 | 4.72 |
| Michael W. Schroeder | 2 | 22 | 4.37 |