Name
Abstract | ||
|---|---|---|
In 2003 Gruttmuller proved that if n >= 3 is odd, then a partial transversal of the Cayley table of Z(n) with length 2 is completable to a transversal. Additionally, he conjectured that a partial transversal of the Cayley table of Z(n) with length k is completable to a transversal if and only if n is odd and either n is an element of {k, k + 1} or n >= 3k - 1. Cavenagh, Hamalainen, and Nelson (in 2009) showed the conjecture is true when k = 3 and n is prime. In this paper, we prove Gruttmuller's conjecture for k = 2 and k = 3 by establishing a more general result for Cayley tables of Abelian groups of odd order. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.37236/9386 | ELECTRONIC JOURNAL OF COMBINATORICS |
DocType | Volume | Issue |
Journal | 28 | 3 |
ISSN | Citations | PageRank |
1077-8926 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jaromy Kuhl | 1 | 10 | 4.72 |
| Donald Mcginn | 2 | 0 | 0.34 |
| Michael William Schroeder | 3 | 0 | 0.68 |