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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.30754 |
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| _version_ | 1866913172097597440 |
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| author | Garoufalidis, Stavros Li, Shana Yunsheng Yu, Josephine |
| author_facet | Garoufalidis, Stavros Li, Shana Yunsheng Yu, Josephine |
| contents | Motivated by the recent work of Harper--Kohli--Song--Tahar, we formulate a positivity, hole-free, and log-concavity conjecture for the Links--Gould polynomial of alternating links and verify it for all 51.3 million alternating knots with at most 19 crossings. All but 544 of those knots satisfy a stronger type-B log-concavity condition characterized by the slopes of edges in the subdivision of the monomial support induced by the log coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30754 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Positivity and log concavity of the Links--Gould polynomial of knots Garoufalidis, Stavros Li, Shana Yunsheng Yu, Josephine Geometric Topology Motivated by the recent work of Harper--Kohli--Song--Tahar, we formulate a positivity, hole-free, and log-concavity conjecture for the Links--Gould polynomial of alternating links and verify it for all 51.3 million alternating knots with at most 19 crossings. All but 544 of those knots satisfy a stronger type-B log-concavity condition characterized by the slopes of edges in the subdivision of the monomial support induced by the log coefficients. |
| title | Positivity and log concavity of the Links--Gould polynomial of knots |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2605.30754 |