Fredman's reciprocity, invariants of Abelian groups, and the permanent of the Cayley table.

DOI10.1007/s10801-010-0236-6zbMath1214.20013arXiv1007.1791OpenAlexW2034643132MaRDI QIDQ617325

Dmitri I. Panyushev

Publication date: 21 January 2011

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

Full work available at URL: https://arxiv.org/abs/1007.1791

zbMATH Keywords

Möbius functionPoincaré seriespermanentsRamanujan sumsEuler totient functionexterior algebrasregular representationsMolien formula

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Ordinary representations and characters (20C15) Vector and tensor algebra, theory of invariants (15A72) Finite abelian groups (20K01) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Actions of groups on commutative rings; invariant theory (13A50)

Related Items (3)

On the number of necklaces whose co-periods divide a given integer ⋮ Circulant matrices and mathematical juggling ⋮ A Reciprocity on Finite Abelian Groups Involving Zero-Sum Sequences

Cites Work

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• The number of terms in the permanent and the determinant of a generic circulant matrix
• Some formulas in invariant theory
• A symmetric relationship for a class of partitions
• Hermite reciprocity for the regular representations of cyclic groups
• Combinatorics of necklaces and ``Hermite reciprocity
• Some properties of circulants
• Invariants of finite groups and their applications to combinatorics
• On the group determinant
• An enumeration problem for a congruence equation
• A Combinatorial Problem on Abelian Groups

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