3 papers
math.GT2026
Characterization of non-self OU sequences of two-component link diagrams
Naoki Sakata, Ayaka Shimizu, Koya Shimokawa
A non-self OU sequence is a cyclic sequence of crossing information of non-self crossings that is obtained by traversing a knot component of an oriented link diagram. In this paper…
math.GT2025
Entanglement statistics of polymers in a lattice tube and unknotting of 4-plats
Nicholas R. Beaton, Kai Ishihara, Mahshid Atapour +4
The Knot Entropy Conjecture states that the exponential growth rate of the number of -edge lattice polygons with knot-type is the same as that for unknot polygons. Moreover,…
math.GT2024
Signature and crossing number of links
Kai Ishihara, Kei Okada, Koya Shimokawa
This paper investigates the relationship between the signature and the crossing number of knots and links. We refine existing theorems and provide a comprehensive classification of…