On subsets of partial difference sets
type: Item
instance of: scholarly article
title: On subsets of partial difference sets
zbMATH Open document ID: 0811.05011
DOI: 10.1016/0012-365X(94)90167-8
author: V. Pereyra
published in: Discrete Mathematics
publication date: 1995-05-03T00:00:00Z
review text: A \((v, k, \lambda, \mu)\)-partial difference set \(D\) is a \(k\)-subset of an abelian group \(G\) of order \(v\) such that \(-D = D\) and the list of differences \(d - d'\) (\(d, d'\in D, d \neq d'\)) contains every nonidentity element in \(D\) exactly \(\lambda\) times and the nonidentity elements not in \(D\) exactly \(\mu\) times. Partial difference sets are a generalization of difference sets with multiplier \(-1\). Extending a result of \textit{R. L. McFarland} [J. Comb. Theory, Ser. A 54, No. 1, 112-122 (1990; Zbl 0728.05012)] the author shows that \(D \cap H\) is a partial difference set in \(H\) if the order of \(H\) and its index in \(G\) are coprime and the index of \(H\) is odd. Some nonexistence results on partial difference sets follow from this theorem.
reviewed by: Alexander Pott
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 562670
zbMATH Keywords: Cayley graph
zbMATH Keywords: strongly regular graph
zbMATH Keywords: difference set
zbMATH Keywords: partial difference sets
MaRDI profile type: Publication
cites work: Q3737429
cites work: Rational G-matrices with rational eigenvalues
cites work: Q5707657
cites work: Q3967545
cites work: Partial difference sets
cites work: Q3818326
cites work: McFarland's conjecture on abelian difference sets with multiplier \(-1\)
cites work: Two addition theorems
cites work: Sub-difference sets of Hadamard difference sets
full work available at URL: 0012-365x(94)90167-8
OpenAlex ID: W2052914304
description: scientific article; zbMATH DE number 562670