{"paper":{"title":"Gaps for the Igusa-Todorov function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gustavo Mata, Gustavo Rama, Marcos Barrios","submitted_at":"2018-10-25T21:53:55Z","abstract_excerpt":"For a finite dimensional algebra $A$ with $0 < \\phi dim (A) = m < \\infty$ we prove that there always exist modules $M$ and $N$ such that $\\phi(M) = m-1$ and $\\phi (N) = 1$. On the other hand, we see an example of an algebra that not every value between $1$ and its $\\phi$-dimension is reached by the $\\phi$ function. We call that values gaps and we prove that the algebras with gaps verifies the finitistic conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12112","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"}