The combinatorics of certain group-invariant mappings: An International Journal

We study combinatorial and number-theoretic issues arising from group-invariant CR mappings from spheres to hyperquadrics. Given an initial complex analytic function, we define two sequences of complex numbers. We derive formulae for these sequences in terms of the Taylor coefficients of the initial...

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Bibliographic Details
Published in:Complex variables and elliptic equations 2013-05, Vol.58 (5), p.621-634
Main Author: D'Angelo, John P.
Format: Article
Language:English
Subjects:
circulants
Combinatorial analysis
Combinatorics
Complex variables
congruences
CR mappings
Derivatives
elementary symmetric functions
finite unitary groups
Functions (mathematics)
generating functions
Invariants
Mapping
Mathematical analysis
polar derivative
Polynomials
resultants
Studies
Citations: Items that this one cites
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Description
Summary:We study combinatorial and number-theoretic issues arising from group-invariant CR mappings from spheres to hyperquadrics. Given an initial complex analytic function, we define two sequences of complex numbers. We derive formulae for these sequences in terms of the Taylor coefficients of the initial function and, in the polynomial case, also in terms of the reciprocals of the roots. We connect these formulae to CR mappings invariant under arbitrary representations of finite cyclic subgroups of the unitary group. We prove that the resultant of the m-th polynomial (which in all cases has integer coefficients) and any of its partial derivatives is divisible by m m .
ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2011.599117