Name
Abstract | ||
|---|---|---|
Let B-p be the Latin square given by the addition table for the integers modulo an odd prime p (i.e. the Cayley table for (Z(p), +)). Here we consider the properties of Latin trades in B-p which preserve orthogonality with one of the p-1 MOLS given by the finite field construction. We show that for certain choices of the orthogonal mate, there is a lower bound logarithmic in p for the number of times each symbol occurs in such a trade, with an overall lower bound of (logp)(2) / log log p for the size of such a trade. Such trades imply the existence of orthomorphisms of the cyclic group which differ from a linear orthomorphism by a small amount. We also show that any transversal in B-p hits the main diagonal either p or at most p - log(2) p - 1 times. Finally, if p equivalent to 1 (mod 6) we show the existence of a Latin square which is orthogonal to B-p and which contains a 2 x 2 subsquare. |
Year | Venue | Keywords |
|---|---|---|
2017 | ELECTRONIC JOURNAL OF COMBINATORICS | Orthogonal array,MOLS,trade,orthomorphism,transversal |
Field | DocType | Volume |
Integer,Prime (order theory),Orthogonal array,Discrete mathematics,Combinatorics,Finite field,Cyclic group,Upper and lower bounds,Transversal (geometry),Mathematics,Main diagonal | Journal | 24 |
Issue | ISSN | Citations |
3 | 1077-8926 | 0 |
PageRank | References | Authors |
0.34 | 1 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nicholas J. Cavenagh | 1 | 92 | 20.89 |
| Diane Donovan | 2 | 72 | 33.88 |
| Fatih Demirkale | 3 | 2 | 2.13 |