Concerning Difference Sets
- 1 January 1953
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 5, 421-424
- https://doi.org/10.4153/cjm-1953-046-6
Abstract
A set of integers {a0, a1, … , an} is said to be a difference set modulo N if the set of differences {ai — aj (i,j = 0, 1, … , n) contains each non-zero residue mod N exactly once. It follows that N and n are connected by the relation N = n2 + n + 1. If {a0, a1 … an} is a difference set mod N, so is the set {a0 + s, a1 + s, … , an + s} (s = 0, 1, … , N). These difference sets form a finite projective plane of N points, with each difference set constituting a line in the plane.Keywords
This publication has 4 references indexed in Scilit:
- Some Theorems on Difference SetsCanadian Journal of Mathematics, 1952
- The Nonexistence of Certain Finite Projective PlanesCanadian Journal of Mathematics, 1949
- Cyclic projective planesDuke Mathematical Journal, 1947
- A theorem in finite projective geometry and some applications to number theoryTransactions of the American Mathematical Society, 1938