{"paper":{"title":"Gap Sequence of Factors of Fibonacci Sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Yuke Huang, Zhiying Wen","submitted_at":"2014-04-16T14:40:22Z","abstract_excerpt":"Let w be a factor of Fibonacci sequence F=x_1x_2..., then it appears in the sequence infinitely many times. Let w_p be the p-th appearance of w and v_{w,p} be the gap between w_p and w_{p+1}. In this paper, we discuss the structure of the gap sequence {v_{w,p}}, we first introduce the singular kernel word sk(w) for any factor w of F and give a decomposition of w with respect to sk(w). Using the singular kernel and the decomposition, we prove the gap sequence {v_{w,p}} has exactly two different elements {v_{w,1},v_{w,2}} and determine the expressions of gaps completely, then we prove that the g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4269","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"}