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A Conway-Coxeter theorem for decorated frieze patterns — arXiv:2609.06029

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.06029
License (as archived): CC0-1.0
Archived: 2026-10-16T14:48:30.758Z
SHA-256 of the archived text: 71f0849396c96b584a76d76dab68d501c5de3f0d46cf194dc35c34041054c7c9
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A Conway-Coxeter theorem for decorated frieze patterns — arXiv:2609.06029 — arXiv (en), https://arxiv.org/abs/2609.06029 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cd3e258d290f (Metraipolis archive dc_cd3e258d290f, sha256 71f0849396c96b584a76d76dab68d501c5de3f0d46cf194dc35c34041054c7c9)

BibTeX

@misc{dccd3e258d290f,
  title = {A Conway-Coxeter theorem for decorated frieze patterns — arXiv:2609.06029},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.06029},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cd3e258d290f; sha256 71f0849396c96b584a76d76dab68d501c5de3f0d46cf194dc35c34041054c7c9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.06029. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $m\geq0$ and put $n=m+3$. We introduce a normalized positive Laurent class of decorated frieze patterns and prove a decorated analogue of the Conway-Coxeter classification theorem. Namely, such friezes of width $m$ are in canonical bijection with weighted triangulations of a convex $n$-gon, whose boundary edges are labeled by independent variables $y_1,\ldots,y_n$ and whose diagonals are labeled by $x_1,\ldots,x_m$. While a weighted Conway-Coxeter propagation algorithm constructs the frieze from a weighted triangulation, a main new ingredient is an explicit nonrecursive Laurent formula expressing each quiddity entry directly from the weighted triangles incident to the corresponding vertex. Conversely, specialization to $1$, Laurent positivity, and a decorated cutting-and-gluing procedure recover the weighted triangulation from the frieze.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.06029 — 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 2026-10-16T14:32:29.773Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).