{"paper":{"title":"Frequencies of subwords in words of linear subword complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Chris Schulz, Jason Bell, Laindon Burnett","submitted_at":"2026-07-30T14:27:02Z","abstract_excerpt":"Using a method of Balkov\\'a--Pelantov\\'a, we show that if ${\\bf w}$ is a right-infinite word over a finite alphabet, then for each nonnegative integer $N$ there are at most $3(p_{\\bf w}(N+1)-p_{\\bf w}(N))+1$ distinct upper (and likewise lower and ordinary when they exist) frequencies for length-$(N+1)$ subwords of ${\\bf w}$, where $p_{\\bf w}(n)$ is the subword complexity function of $n$. In particular, this gives a uniform upper bound when ${\\bf w}$ has linearly bounded subword complexity. We provide examples showing that whenever $f(n)$ is a weakly increasing function tending to infinity, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28273","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.28273/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}