Cycle indices of linear, affine, and projective groups

DOI10.1016/S0024-3795(96)00530-7zbMath0891.20001WikidataQ29541753 ScholiaQ29541753MaRDI QIDQ1368764

Harald Fripertinger

Publication date: 19 July 1998

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

general linear groupssymmetric groupsaffine groupsfinite group actionsnumbers of cyclesfinite \(G\)-setscycle indicesisometry classes of linear codes

Mathematics Subject Classification ID

Related Items (14)

Coset-wise affine functions and cycle types of complete mappings ⋮ Combinatorial families enumerated by quasi-polynomials ⋮ Enumeration of orbits on cycles for linear and affine groups ⋮ A general construction of regular complete permutation polynomials ⋮ Orbits of rational \(n\)-sets of projective spaces under the action of the linear group ⋮ The number of affine equivalent classes and extended affine equivalent classes of vectorial Boolean functions ⋮ Random matrix theory over finite fields ⋮ Isometry classes of codes arising from sets of points in the projective plane ⋮ Isometry classes of codes arising from sets of points in the projective plane ⋮ Asymptotic numbers of non-equivalent codes in three notions of equivalence ⋮ Isotopic classes of transversals in dihedral group \(D_{2n}\), \(n\) odd ⋮ Some Characterizations of a Normal Subgroup of a Group and Isotopic Classes of Transversals ⋮ Metacommutation of primes in central simple algebras ⋮ Metacommutation of primes in Eichler orders

Uses Software

• SYMMETRICA

Cites Work

• The cycle structure of a linear transformation over a finite field
• Consequences of the Brylawski-Lucas theorem for binary matroids
• The Characters of the Finite General Linear Groups
• On the Classification of Boolean Functions by the General Linear and Affine Groups
• On the cycle index of a product of permutation groups
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