{"paper":{"title":"Irreducibility of the Cayley-Menger determinant, and of a class of related polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bach Nguyen, Mostafa Hayajneh, Mowaffaq Hajja, Shadi Shaqaqha","submitted_at":"2017-01-02T14:39:32Z","abstract_excerpt":"If $S$ is a given regular $n$-simplex, $n \\ge 2$, of edge length $a$, then the distances $a_1$, $\\cdots$, $a_{n+1}$ of an arbitrary point in its affine hull to its vertices are related by the fairly known elegant relation $\\phi_{n+1} (a,a_1,\\cdots,a_{n+1})=0$, where $$\\phi = \\phi_t (x, x_1,\\cdots,x_{n+1}) = \\left( x^2+x_1^2+\\cdots+x_{n+1}^2\\right)^2 - t\\left( x^4+x_1^4+\\cdots+x_{n+1}^4\\right).$$ The natural question whether this is essentially the only relation is answered positively by M. Hajja, M. Hayajneh, B. Nguyen, and Sh. Shaqaqha in a recently submitted paper entitled \"Distances from th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00407","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}