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Yuya Nishimura

Publications and source records attributed to Yuya Nishimura.

4 recordsLinked to original sources
arXiv2025

Quantum enhancement polynomials associated with the canonical two-element tricbracket

Quantum enhancement polynomials are invariants for oriented links, defined in association with an algebraic structure called a tribracket. In this paper, we focus on the particular case of the canonical two-element tribracket. We prove that, in that case, the quantum enhancement polynomials can be recovered by five specific polynomials, which we refer to as the universal quantum enhancement polynomials. After presenting several notable properties of these polynomials, we show that they are strictly stronger than the Jones polynomial. Furthermore, we provide computational results for links with up to 10 crossings.

math.GT↗
arXiv2023

The computational complexity of the solid torus core recognition problem

The solid torus core recognition problem is the problem that, given a knot in the solid tours, decides whether the knot is the core of the solid torus. That problem is in NP since the thickened torus recognition problem is in NP. We give an alternate proof of that fact and prove that the problem is in co-NP. It is also proved that the Hopf link recognition problem is in NP and co-NP as a corollary of this result.

math.GT↗
arXiv2022

The Computational Complexity of Classical Knot Recognition

The classical knot recognition problem is the problem of determining whether the virtual knot represented by a given diagram is classical. We prove that this problem is in NP, and we give an exponential time algorithm for the problem.

math.GT↗