New necessary conditions on (negative) Latin square type partial difference sets in abelian groups

DOI10.1016/j.jcta.2019.105208zbMath1433.05056arXiv1905.03730OpenAlexW3000062557WikidataQ126398235 ScholiaQ126398235MaRDI QIDQ2299649

Zeying Wang

Publication date: 21 February 2020

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.03730

zbMATH Keywords

partial difference setstrongly regular Cayley graphLatin and negative Latin square type PDS

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Finite abelian groups (20K01) Orthogonal arrays, Latin squares, Room squares (05B15) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10)

Related Items (3)

Packings of partial difference sets ⋮ Restrictions on parameters of partial difference sets in nonabelian groups ⋮ New constructions of strongly regular Cayley graphs on abelian non \(p\)-groups

Cites Work

• Paley type partial difference sets in non \(p\)-groups
• Translation nets and fixed-point-free group automorphisms
• Some implications on amorphic association schemes
• Amorphic association schemes with negative Latin square-type graphs
• New negative Latin square type partial difference sets in nonelementary Abelian 2-groups and 3-groups
• On subsets of partial difference sets
• A survey of partial difference sets
• Strongly regular decompositions of the complete graph
• Paley partial difference sets in groups of order \(n^{4}\) and \(9n^{4}\) for any odd \(n>1\)
• Proper partial geometries with Singer groups and pseudogeometric partial difference sets
• Negative Latin square type partial difference sets and amorphic association schemes with Galois rings
• NEGATIVE LATIN SQUARE TYPE PARTIAL DIFFERENCE SETS IN NONELEMENTARY ABELIAN 2-GROUPS

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