{
  "abstract": "Consider a sequence of i.i.d.~trials $X=\\{X_1, X_2, \\ldots, X_n\\}$ where $p(X_i=j)={1}/{d}; j=1,2,\\ldots, d$, or more generally $p(X_i=j)=p_j; \\sum_{1\\le j\\le d}p_j=1$. We consider the variable $D$ that counts the number of distinct substrings of all lengths,$1\\le k\\le n$ in $X$ and prove results concerning $E(D)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19409",
  "author_total": 1,
  "authors": [
    {
      "name": "Anant Godbole"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/61vzhddtfpzgv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19409",
  "fulltext_url": null,
  "id": "61vzhddtfpzgv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19409",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19409",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/61vzhddtfpzgv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19409",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19409"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Expected Number of Distinct Substrings in an Alphabet String",
  "title_text": "The Expected Number of Distinct Substrings in an Alphabet String",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/61vzhddtfpzgv",
  "venue": "arXiv",
  "versions": []
}