{
  "abstract": "This work considers combinatorial and statistical aspects of {\\em{shifts of finite type}}, which are families of words over a finite alphabet which avoid a fixed class of {\\emph{forbidden}} sub-words. The overarching question we are interested in is: how do local statistics of a uniformly random element of the shift space depend on combinatorial features of the forbidden set? We focus on the binary alphabet $\\{0,1\\}$, the class of shift spaces where a single pattern is forbidden, and the average frequency of $1$s (equivalently, the probability of observing $1$ at a given position). In this case, the relevant combinatorial information is encoded by a two-variable auto-correlation polynomial associated to the forbidden word, which we call the {\\em{border polynomial}}. We present several results and examples characterizing the ordering of all words by their letter frequencies: for example, we describe the set of patterns which, when forbidden, cause the frequency of $1$s to increase, decrease, or stay exactly $1/2$. Our methodologies include novel explicit local injections and bijections, generating function analysis, and a connection with a probabilistic notion of letter frequency.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.06655",
  "author_total": 3,
  "authors": [
    {
      "name": "Miklós Bóna"
    },
    {
      "name": "Balázs Maga"
    },
    {
      "name": "Jacob Richey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/39540xbgyg6mb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.06655",
  "fulltext_url": null,
  "id": "39540xbgyg6mb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.06655",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7163867644",
  "pdf_url": "https://arxiv.org/pdf/2606.06655",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/39540xbgyg6mb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2606.06655",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.06655"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Letter frequency in shifts of finite type with one forbidden word",
  "title_text": "Letter frequency in shifts of finite type with one forbidden word",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/39540xbgyg6mb",
  "venue": "arXiv",
  "versions": []
}