{"paper":{"title":"The structure of palindromes in the Fibonacci sequence and some applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Yuke Huang, Zhiying Wen","submitted_at":"2016-01-18T03:22:22Z","abstract_excerpt":"Let ${\\cal P}$ be the set of palindromes occurring in the Fibonacci sequence. In this note, we establish three structures of $\\mathcal{P}$ and and discuss their properties: cylinder structure, chain structure and recursive structure. Using these structures, we determine that the number of distinct palindrome occurrences in $\\mathbb{F}[1,n]$ is exactly $n$, where $\\mathbb{F}[1,n]$ is the prefix of the Fibonacci sequence of length $n$. Then we give an algorithm for counting the number of repeated palindrome occurrences in $\\mathbb{F}[1,n]$, and get explicit expressions for some special $n$, whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04391","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"}