{"paper":{"title":"Counting the minimal number of inflections of a plane curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DG","authors_text":"Gleb Nenashev","submitted_at":"2014-02-23T19:55:37Z","abstract_excerpt":"Given a plane curve $\\gamma: S^1\\to \\mathbb R^2$, we consider the problem of determining the minimal number $I(\\gamma)$ of inflections which curves $\\mbox{diff}(\\gamma)$ may have, where $\\mbox{diff}$ runs over the group of diffeomorphisms of $\\mathbb R^2$. We show that if $\\gamma$ is an immersed curve with $D(\\gamma)$ double points and no other singularities, then $I(\\gamma)\\leq 2D(\\gamma)$. In fact, we prove the latter result for the so-called plane doodles which are finite collections of closed immersed plane curves whose only singularities are double points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5659","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"}