{"paper":{"title":"The Strong Factorial Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Arno van den Essen, Eric Edo","submitted_at":"2013-04-14T23:51:43Z","abstract_excerpt":"In this paper we present an unexpected link between the Factorial Conjecture and Furter's Rigidity Conjecture. The Factorial Conjecture in dimension $m$ asserts that if a polynomial $f$ in $m$ variables $X_i$ over $\\C$ is such that ${\\cal L}(f^k)=0$ for all $k\\geq 1$, then $f=0$, where ${\\cal L}$ is the $\\C$-linear map from $\\C[X_1,...,X_m]$ to $\\C$ defined by ${\\cal L}(X_1^{l_1}... X_m^{l_m})=l_1!... l_m!$. The Rigidity Conjecture asserts that a univariate polynomial map $a(X)$ with complex coefficients of degree at most $m+1$ such that $a(X)=X$ mod $X^2$, is equal to $X$ if $m$ consecutive c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3956","kind":"arxiv","version":2},"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"}