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math.GT2026
The knot polynomial
Stavros Garoufalidis, Shana Yunsheng Li
We present the knot polynomial associated to the 12-dimensional sporadic Nichols algebra with automorphism, compute it for all knots with 16 crossings and di…
math.GT2026
Fixed-parameter tractable computation of Reshetikhin--Turaev knot polynomials via tensor networks
Shana Yunsheng Li
We give a thorough analysis of the time complexity of computing Reshetikhin--Turaev knot polynomials via tensor contractions on the associated tensor networks, showing that the com…
math.GT2026
Positivity and log concavity of the Links--Gould polynomial of knots
Stavros Garoufalidis, Shana Yunsheng Li, Josephine Yu
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…