The Solution of the Waterloo Problem
Document Type
Article
Publication Date
8-1-1995
Abstract
Let D(d, q) be a classical (ν, k, λ)-Singer difference set in a cyclic group G corresponding to the complement of the point-hyperplane design of PG(d, q) (d ⩾ 1). We characterize those Singer difference sets D(d, q) which admit a “Waterloo decomposition” D = A ∪ B such that (A − B) · (A − B)(−1) = k inZG: Theorem. D(d, q) admits a Waterloo decomposition if and only if d is even.
Repository Citation
Arasu, K. T.,
Dillon, J. F.,
Jungnickel, D.,
& Pott, A.
(1995). The Solution of the Waterloo Problem. Journal of Combinatorial Theory. Series A, 71 (2), 316-331.
https://corescholar.libraries.wright.edu/math/576
DOI
10.1016/0097-3165(95)90006-3
