### Abstract

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}.

Original language | English (US) |
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Pages (from-to) | 621-634 |

Number of pages | 14 |

Journal | Complex Variables and Elliptic Equations |

Volume | 58 |

Issue number | 5 |

DOIs | |

State | Published - May 1 2013 |

### Keywords

- CR mappings
- circulants
- congruences
- elementary symmetric functions
- finite unitary groups
- generating functions
- polar derivative
- polynomials
- resultants

### ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics

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## Cite this

D'Angelo, J. P. (2013). The combinatorics of certain group-invariant mappings.

*Complex Variables and Elliptic Equations*,*58*(5), 621-634. https://doi.org/10.1080/17476933.2011.599117