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The Expected Number of Distinct Substrings in an Alphabet String — arXiv:2609.19409

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.19409
License (as archived): CC0-1.0
Archived: 2026-10-10T04:23:35.191Z
SHA-256 of the archived text: 7d5339c7bbdf3ca8266e243d533aeb83425d20892feb8693d66680f5b46b590e
Stable URL of this page: https://metraipolis.com/documento/dc_debbbfa3a4ad

How to cite

The Expected Number of Distinct Substrings in an Alphabet String — arXiv:2609.19409 — arXiv (en), https://arxiv.org/abs/2609.19409 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_debbbfa3a4ad (Metraipolis archive dc_debbbfa3a4ad, sha256 7d5339c7bbdf3ca8266e243d533aeb83425d20892feb8693d66680f5b46b590e)

BibTeX

@misc{dcdebbbfa3a4ad,
  title = {The Expected Number of Distinct Substrings in an Alphabet String — arXiv:2609.19409},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.19409},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_debbbfa3a4ad; sha256 7d5339c7bbdf3ca8266e243d533aeb83425d20892feb8693d66680f5b46b590e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.19409. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $E(D)$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-18 in math.PR).
Categorie arXiv: Probability (math.PR) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.19409 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T04:09:58.338Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).