{"paper":{"title":"Dual numbers, weighted quivers, and extended Somos and Gale-Robinson sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Serge Tabachnikov, Valentin Ovsienko","submitted_at":"2017-05-03T21:05:17Z","abstract_excerpt":"We investigate a general method that allows one to construct new integer sequences extending existing ones. We apply this method to the classic Somos-4 and Somos-5, and the Gale-Robinson sequences, as well as to more general class of sequences introduced by Fordy and Marsh, and produce a great number of new sequences. The method is based on the notion of \"weighted quiver\", a quiver with a $\\mathbb Z$-valued function on the set of vertices that obeys very special rules of mutation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01623","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"}