{"paper":{"title":"Duplication Distance to the Root for Binary Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.IT","q-bio.GN"],"primary_cat":"cs.IT","authors_text":"Farzad Farnoud, Jehoshua Bruck, Noga Alon, Siddharth Jain","submitted_at":"2016-11-17T02:39:54Z","abstract_excerpt":"We study the tandem duplication distance between binary sequences and their roots. In other words, the quantity of interest is the number of tandem duplication operations of the form $\\seq x = \\seq a \\seq b \\seq c \\to \\seq y = \\seq a \\seq b \\seq b \\seq c$, where $\\seq x$ and $\\seq y$ are sequences and $\\seq a$, $\\seq b$, and $\\seq c$ are their substrings, needed to generate a binary sequence of length $n$ starting from a square-free sequence from the set $\\{0,1,01,10,010,101\\}$. This problem is a restricted case of finding the duplication/deduplication distance between two sequences, defined a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05537","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"}