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On Correspondences between the Alexander Polynomials of Special Alternating Links and MOY Graphs

  • Leonardo Rodrigues de Medeiros
  • Arker Oke Soe
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Abstract

Fox's conjecture famously asserts that the absolute values of the coefficients of the Alexander polynomial of alternating links are trapezoidal. In the setting of MOY graphs, where a different notion of Alexander polynomial appears, the equivalent result to Fox's conjecture is known to hold. In this paper, we relate the two polynomials in the case of special alternating links. More precisely, we show that their degrees, first, and last coefficient agree, and that the MOY polynomial coefficients always dominate the classical Alexander polynomial.

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Cite

BibTeXRIS
BibTeX
@misc{medeiros2026correspondences,
  title = {{On Correspondences between the Alexander Polynomials of Special Alternating Links and MOY Graphs}},
  author = {Leonardo Rodrigues de Medeiros and Arker Oke Soe},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14809},
  eprint = {2609.14809},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14809},
}
RIS
TY  - UNPB
TI  - On Correspondences between the Alexander Polynomials of Special Alternating Links and MOY Graphs
AU  - Leonardo Rodrigues de Medeiros
AU  - Arker Oke Soe
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14809
UR  - https://arxiv.org/abs/2609.14809
AB  - Fox's conjecture famously asserts that the absolute values of the coefficients of the Alexander polynomial of alternating links are trapezoidal. In the setting of MOY graphs, where a different notion of Alexander polynomial appears, the equivalent result to Fox's conjecture is known to hold. In this paper, we relate the two polynomials in the case of special alternating links. More precisely, we show that their degrees, first, and last coefficient agree, and that the MOY polynomial coefficients always dominate the classical Alexander polynomial.
ER  -