Forced Polynomial Identities and the Uniqueness of (7,5,3) in the Lambda-Ring of M24
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2026
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| _version_ | 1866901135051194368 |
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| author | Lyons, Ronney |
| author_facet | Lyons, Ronney |
| contents | <p>MathNote E in the M24 Lambda-Ring Engine series. Proves that symmetric and exterior power characters of the deleted permutation representation chi_23 of M24 satisfy forced polynomial identities whose residuals all vanish at a single isolated point. At class 3A, twelve engine values through degree 8 are determined by chi alone, with x=5 as the unique positive rational root of each residual. At class 2A, three identities isolate x=7. At class 5A, two identities isolate x=3 including the exact vanishing W4(5A)=0. A cross-class constraint proves (7,5,3) is the unique real solution. All polynomials verified by GAP in SageMath.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19275712 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Forced Polynomial Identities and the Uniqueness of (7,5,3) in the Lambda-Ring of M24 Lyons, Ronney symmetric powers Newton-Girard deleted permutation polynomial uniqueness forced identities lambda-ring Mathieu group M24 <p>MathNote E in the M24 Lambda-Ring Engine series. Proves that symmetric and exterior power characters of the deleted permutation representation chi_23 of M24 satisfy forced polynomial identities whose residuals all vanish at a single isolated point. At class 3A, twelve engine values through degree 8 are determined by chi alone, with x=5 as the unique positive rational root of each residual. At class 2A, three identities isolate x=7. At class 5A, two identities isolate x=3 including the exact vanishing W4(5A)=0. A cross-class constraint proves (7,5,3) is the unique real solution. All polynomials verified by GAP in SageMath.</p> |
| title | Forced Polynomial Identities and the Uniqueness of (7,5,3) in the Lambda-Ring of M24 |
| topic | symmetric powers Newton-Girard deleted permutation polynomial uniqueness forced identities lambda-ring Mathieu group M24 |
| url | https://doi.org/10.5281/zenodo.19275712 |