{"paper":{"title":"Potentials of a Frobenius like structure and $m$ bases of a vector space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","nlin.SI"],"primary_cat":"math.AG","authors_text":"Alexander Varchenko, Claus Hertling","submitted_at":"2016-08-30T12:33:29Z","abstract_excerpt":"This paper proves the existence of potentials of the first and second kind of a Frobenius like structure in a frame which encompasses families of arrangements.\n  Surprisingly the proof is based on the study of finite sets of vectors in a finite-dimensional vector space $V$. Given a natural number $m$ and a finite set $(v_i)$ of vectors we give a necessary and sufficient condition to find in the set $(v_i)$ $m$ bases of $V$. If $m$ bases in $(v_i)$ can be selected, we define elementary transformations of such a selection and show that any two selections are connected by a sequence of elementary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08423","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"}