Number Theoretic Consequences on the Parameters of a Symmetric Design
Document Type
Article
Publication Date
5-1-1987
Identifier/URL
41072135 (Pure)
Abstract
A well-known necesary condition for the existence of a 2-(v,k,λ)symmetric design is that k(k−1)=λ(v−1). The author proves that fora fixed λ, this equation has only finitely many solutions with theproperty that v satisfies one of the following conditions below:(i) For a fixed set S of primes, v is divisible only by primes in S;(ii) v is a perfect nth power (n≥3); (iii) vλ is a square.Also, in the case when λ=2n−2an, a weak upper bound on k isobtained.
Repository Citation
Arasu, K. T.
(1987). Number Theoretic Consequences on the Parameters of a Symmetric Design. Discrete Mathematics, 65 (1), 1-4.
https://corescholar.libraries.wright.edu/math/521
DOI
10.1016/0012-365X(87)90206-8
