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Wild frieze patterns over the integers

  • Leon Eickhoff
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Abstract

We study frieze patterns over the integers that are allowed to have wild entries. We introduce the quiddity number as a new invariant. The quiddity number is then used to classify strongly connected components of the directed graph Γ2,n(ℤ). Furthermore, we show that every finite simple directed graph arises as an induced subgraph of a directed graph Γ2,n(ℤ) for n sufficiently large.

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Cite

BibTeXRIS
BibTeX
@misc{eickhoff2026wild,
  title = {{Wild frieze patterns over the integers}},
  author = {Leon Eickhoff},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.20967},
  eprint = {2609.20967},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20967},
}
RIS
TY  - UNPB
TI  - Wild frieze patterns over the integers
AU  - Leon Eickhoff
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.20967
UR  - https://arxiv.org/abs/2609.20967
AB  - We study frieze patterns over the integers that are allowed to have wild entries. We introduce the quiddity number as a new invariant. The quiddity number is then used to classify strongly connected components of the directed graph Γ_2,n(ℤ). Furthermore, we show that every finite simple directed graph arises as an induced subgraph of a directed graph Γ_2,n(ℤ) for n sufficiently large.
ER  -