Counting Schur rings over cyclic groups

DOI10.1007/s10801-019-00870-1OpenAlexW2247371140WikidataQ128545089 ScholiaQ128545089MaRDI QIDQ2304197

Andrew Misseldine

Publication date: 6 March 2020

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.03757

zbMATH Keywords

Catalan numbercyclotomic fieldcyclic groupPORC conjectureSchröder numberSchur ring

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Association schemes, strongly regular graphs (05E30) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Cyclotomic extensions (11R18)

Uses Software

• Magma
• OEIS

Cites Work

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• The number of indecomposable Schur rings over a cyclic 2-group.
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• On the structure of basic sets of Schur rings over cyclic groups
• The Magma algebra system. I: The user language
• The structure of Schur rings over cyclic groups
• Groups and nilpotent Lie rings whose order is the sixth power of a prime.
• On Schur rings over cyclic groups. II
• Non-PORC behaviour of a class of descendant \(p\)-groups.
• Counting circulant graphs of prime-power order by decomposing into orbit enumeration problems
• The groups with order \(p^7\) for odd prime \(p\).
• Zur Theorie der einfach transitiven Permutationsgruppen. II
• Enumeration of Schur Rings Over Small Groups
• Enumerating p -Groups. I: Inequalities
• Higman's PORC conjecture for a family of groups
• Enumeration of groups of prime-power order
• Enumerating p -Groups, II: Problems Whose Solution is PORC

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