{"paper":{"title":"On Generating Binary Words Palindromically","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"L.Q. Zamboni, Mari Huova, Tero Harju","submitted_at":"2013-09-07T17:26:34Z","abstract_excerpt":"We regard a finite word $u=u_1u_2\\cdots u_n$ up to word isomorphism as an equivalence relation on $\\{1,2,\\ldots, n\\}$ where $i$ is equivalent to $j$ if and only if $x_i=x_j.$ Some finite words (in particular all binary words) are generated by \"{\\it palindromic}\" relations of the form $k\\sim j+i-k$ for some choice of $1\\leq i\\leq j\\leq n$ and $k\\in \\{i,i+1,\\ldots,j\\}.$ That is to say, some finite words $u$ are uniquely determined up to word isomorphism by the position and length of some of its palindromic factors. In this paper we study the function $\\mu(u)$ defined as the least number of palin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1886","kind":"arxiv","version":2},"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"}