18 citations · 63 across the 14 of their papers we have counts for
14 papers
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…
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…
Non-integral boundary slopes of alternating knots
Masaharu Ishikawa, Thomas W. Mattman, Koya Shimokawa
We show, for every positive integer , there is an alternating knot having a boundary slope with denominator . We make use of Kabaya's method for boundary slopes and the layer…
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,…
Handlebody decompositions of 3-manifolds and polycontinuous patterns
Naoki Sakata, Ryosuke Mishina, Masaki Ogawa +4
We introduce the concept of a handlebody decomposition of a 3-manifold, a generalization of a Heegaard splitting, or a trisection. We show that two handlebody decompositions of a c…
Alternating knots with large boundary slope diameter
Masaharu Ishikawa, Thomas W. Mattman, Kazuya Namiki +1
We show that, for an alternating knot, the ratio of the diameter of the set of boundary slopes to the crossing number can be arbitrarily large.