Group-theoretical generalization of necklace polynomials

DOI10.1007/s10801-011-0307-3zbMath1376.05008OpenAlexW2058746048MaRDI QIDQ1686123

Young-Tak Oh

Publication date: 21 December 2017

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

Full work available at URL: https://doi.org/10.1007/s10801-011-0307-3

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Subgroup theorems; subgroup growth (20E07) Special aspects of infinite or finite groups (20F99)

Cites Work

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• The formal series Witt transform
• The Burnside ring of the infinite cyclic group and its relations to the necklace algebra, \(\lambda\)-rings, and the universal ring of Witt vectors
• The Burnside ring of profinite groups and the Witt vector construction
• \(R\)-analogue of the Burnside ring of profinite groups and free Lie algebras
• \(\lambda\)-rings and the representation theory of the symmetric group
• Witt vectors and the algebra of necklaces
• \(q\)-analog of the Möbius function and the cyclotomic identity associated to a profinite group.
• \(q\)-deformed necklace rings and \(q\)-Möbius function
• Formal group-theoretic generalizations of the necklace algebra, including a \(q\)-deformation
• Finite index subgroups in profinite groups.
• An extension of the exponential formula in enumerative combinatorics
• \(q\)-deformation of Witt-Burnside rings
• Necklace rings and logarithmic functions
• Group representations, \(\lambda\)-rings and the \(J\)-homomorphism
• The Free Lie Ring and Lie Representations of the Full Linear Group

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