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PreprintCC BY-SA 4.0arXiv

Short Paper No. 1: Relation between integer sequence A319433 and the maximum degrees of finite linear Jaco graphs

  • Timothée Raso
  • Johan Kok
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Abstract

This short paper presents the interesting relation between integer sequence A319433 in https://oeis.org and the maximum degrees of the family of finite linear Jaco graphs Jn(x) where n = 1,2,3,…. The result first appeared as a conjecture. Subsequently, a proof through AI-assisted mathematical reasoning came to the fore. Appropriate clarity remarks follow in the main text. It appears that Golden ratio-like floor function plays an important role in the analysis of the graph structural properties of the family of finite linear Jaco graphs.

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Cite

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BibTeX
@misc{raso2026short,
  title = {{Short Paper No. 1: Relation between integer sequence A319433 and the maximum degrees of finite linear Jaco graphs}},
  author = {Timothée Raso and Johan Kok},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01554},
  eprint = {2611.01554},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01554},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Short Paper No. 1: Relation between integer sequence A319433 and the maximum degrees of finite linear Jaco graphs
AU  - Timothée Raso
AU  - Johan Kok
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01554
UR  - https://arxiv.org/abs/2611.01554
AB  - This short paper presents the interesting relation between integer sequence A319433 in https://oeis.org and the maximum degrees of the family of finite linear Jaco graphs J_n(x) where n = 1,2,3,…. The result first appeared as a conjecture. Subsequently, a proof through AI-assisted mathematical reasoning came to the fore. Appropriate clarity remarks follow in the main text. It appears that Golden ratio-like floor function plays an important role in the analysis of the graph structural properties of the family of finite linear Jaco graphs.
ER  -