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arXiv · 2504.16611

Forms of Nice Functions

Anthony G. O'Farrell
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Abstract

You can invent striking and challenging problems with unique solution by building some symmetry into functional equations. Some are suitable for high school; others could generate college-level projects involving computer algebra. The problems are functional equations with group actions in the background. Interesting examples arise even from small finite groups. Whether a given problem ``works" with a given choice of constant coefficients depends on whether a related multilinear form is nonzero. These forms are essentially the classical group determinants studied by Frobenius in the nineteenth century.

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Anthony G. O'Farrell. 2025-04-23. Forms of Nice Functions. https://doi.org/10.1080/07468342.2025.2485013

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