{"paper":{"title":"The intersection of subgroups in free groups and linear programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.OC"],"primary_cat":"math.GR","authors_text":"Sergei V. Ivanov","submitted_at":"2016-07-28T03:27:56Z","abstract_excerpt":"We study the intersection of finitely generated subgroups of free groups by utilizing the method of linear programming. We prove that if $H_1$ is a finitely generated subgroup of a free group $F$, then the WN-coefficient $\\sigma(H_1)$ of $H_1$ is rational and can be computed in deterministic exponential time in the size of $H_1$. This coefficient $\\sigma(H_1)$ is the minimal nonnegative real number such that, for every finitely generated subgroup $H_2$ of $F$, it is true that $\\bar {\\rm r}(H_1, H_2) \\le \\sigma(H_1) \\bar {\\rm r}(H_1) \\bar {\\rm r}(H_2)$, where $\\bar{ {\\rm r}} (H) := \\max ( {\\rm "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08303","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"}