{"paper":{"title":"Generalized trapezoidal words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Amy Glen, Florence Lev\\'e","submitted_at":"2014-08-03T03:18:45Z","abstract_excerpt":"The factor complexity function $C_w(n)$ of a finite or infinite word $w$ counts the number of distinct factors of $w$ of length $n$ for each $n \\ge 0$. A finite word $w$ of length $|w|$ is said to be trapezoidal if the graph of its factor complexity $C_w(n)$ as a function of $n$ (for $0 \\leq n \\leq |w|$) is that of a regular trapezoid (or possibly an isosceles triangle); that is, $C_w(n)$ increases by 1 with each $n$ on some interval of length $r$, then $C_w(n)$ is constant on some interval of length $s$, and finally $C_w(n)$ decreases by 1 with each $n$ on an interval of the same length $r$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0451","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"}