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Counting in Vieta graphs over $\mathbb{F}_p$ — arXiv:2608.03097

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.03097
License (as archived): CC0-1.0
Archived: 2026-10-31T12:55:57.264Z
SHA-256 of the archived text: 331e8dd34af3272a9f3957f4b5f1a4191932dcd1352fff64bf0a559f23419ab9
Stable URL of this page: https://metraipolis.com/documento/dc_fbbd2d941fe7

How to cite

Counting in Vieta graphs over $\mathbb{F}_p$ — arXiv:2608.03097 — arXiv (en), https://arxiv.org/abs/2608.03097 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fbbd2d941fe7 (Metraipolis archive dc_fbbd2d941fe7, sha256 331e8dd34af3272a9f3957f4b5f1a4191932dcd1352fff64bf0a559f23419ab9)

BibTeX

@misc{dcfbbd2d941fe7,
  title = {Counting in Vieta graphs over $mathbbF_p$ — arXiv:2608.03097},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.03097},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fbbd2d941fe7; sha256 331e8dd34af3272a9f3957f4b5f1a4191932dcd1352fff64bf0a559f23419ab9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.03097. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We introduce and study a finite simple graph of algebraic origin: the Vieta graph on the solution set over $\mathbb{F}_p$ to a symmetric, multivariate equation which is quadratic in each variable. This construction is a broad generalization of the Markoff graph over $\mathbb{F}_p$, extensively studied in the recent literature. We give a systematic approach, partly based on quadratic character sums, to the following basic counting questions: how many vertices does a Vieta graph have, and what is the degree distribution? We focus on explicit counts, addressing the low-dimensional cases in three and four variables.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-05 in math.CO).
Categorie arXiv: Number Theory (math.NT) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2608.03097 — 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 2026-10-31T12:42:47.791Z dalla pagina https://arxiv.org/catchup/math.CO/2026-08-05?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).