15 citations · 81 across the 53 of their papers we have counts for
54 papers
Two-tone colorings and surjective dihedral representations for links
Kazuhiro Ichihara, Katsumi Ishikawa, Eri Matsudo +1
It is well-known that a knot is Fox -colorable for a prime if and only if the knot group admits a surjective homomorphism to the dihedral group of degree . However, this…
The Computational Complexity of Classical Knot Recognition
Kazuhiro Ichihara, Yuya Nishimura, Seiichi Tani
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…
Constructing Goeritz matrix from Dehn coloring matrix
Masaki Horiuchi, Kazuhiro Ichihara, Eri Matsudo +1
Associated to a knot diagram, Goeritz introduced an integral matrix, which is now called a Goeritz matrix. It was shown by Traldi that the solution space of the equations with Goer…
On constraints for knots to admit chirally cosmetic surgeries and their calculations
Kazuhiro Ichihara, Tetsuya Ito, Toshio Saito
We discuss various constraints for knots in to admit chirally cosmetic surgeries, derived from invariants of 3-manifolds, such as, the quantum -invariant, the rank o…
Coloring links by the symmetric group of degree three
Kazuhiro Ichihara, Eri Matsudo
We consider the number of colors for the colorings of links by the symmetric group of degree . For knots, such a coloring corresponds to a Fox 3-coloring, and thus the num…
Knots in homology lens spaces determined by their complements
Kazuhiro Ichihara, Toshio Saito
In this paper, we consider the knot complement problem for not null-homologous knots in homology lens spaces. Let be a homology lens space with $H_1(M; \mathbb{Z}) \cong \mathb…