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New research shows exponential decay in link invariant detection probabilities

By PulseAugur Editorial · [1 sources] ·

A new research paper published on arXiv details the exponential decay in detection probabilities for link invariants among prime alternating links. The study, authored by Daniel Tubbenhauer, demonstrates that for many standard link invariants, including the Jones and HOMFLYPT polynomials and integral Khovanov homology, the proportion of distinct invariant values and their detection probability decrease exponentially with the number of crossings. This phenomenon indicates that most such links belong to an invariant fiber whose size also grows exponentially with the number of crossings. AI

RANK_REASON The cluster contains a single academic paper published on arXiv detailing mathematical research. [lever_c_demoted from research: ic=1 ai=0.1]

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New research shows exponential decay in link invariant detection probabilities

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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Tuomas Kelom\"aki, Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz, Victor L. Zhang ·

    On detection probabilities of link invariants

    arXiv:2509.05574v3 Announce Type: replace-cross Abstract: We prove that, for many standard link invariants, both the proportion of distinct invariant values and the detection probability among prime alternating links with at most n crossings decay exponentially in n, with an expl…

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