\(q\)-deformed necklace rings and \(q\)-Möbius function

DOI10.1016/j.jalgebra.2008.05.016zbMath1159.05003OpenAlexW2015481289MaRDI QIDQ948723

Young-Tak Oh

Publication date: 17 October 2008

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2008.05.016

zbMATH Keywords

Möbius functioncyclotomic identitynecklace ringrestricted Lie \(p\)-algebra

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Identities, free Lie (super)algebras (17B01) Modular Lie (super)algebras (17B50)

Related Items

Decomposition of the Witt-Burnside ring and Burnside ring of an abelian profinite group ⋮ Group-theoretical generalization of necklace polynomials ⋮ \(q\)-deformations of statistical mechanical systems and motives over finite fields

Cites Work

• 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
• Witt vectors and the algebra of necklaces
• Nested Witt vectors and their \(q\)-deformation
• Classification of the ring of Witt vectors and the necklace ring associated with the formal group law \(X+Y - qXY\)
• Formal group-theoretic generalizations of the necklace algebra, including a \(q\)-deformation
• Witt's formula for restricted Lie algebras.
• An extension of the exponential formula in enumerative combinatorics
• \(q\)-deformation of Witt-Burnside rings
• Necklace rings and logarithmic functions
• Aperiodic rings, necklace rings, and Witt vectors
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