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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2504.16611 |
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| _version_ | 1866910917281710080 |
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| author | O'Farrell, Anthony G. |
| author_facet | O'Farrell, Anthony G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Forms of Nice Functions O'Farrell, Anthony G. Group Theory 39-01 (Primary) 20-01 (Secondary) 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. |
| title | Forms of Nice Functions |
| topic | Group Theory 39-01 (Primary) 20-01 (Secondary) |
| url | https://arxiv.org/abs/2504.16611 |