5 citations · 5 across the 10 of their papers we have counts for
11 papers
The minimum number of Dehn -colors of any nonsplittable -colorable link is three
Eri Matsudo, Kanako Oshiro
Our previous papers [8, 9] are the first and second to discuss minimum numbers of ``region'' colors, while minimum numbers of arc colors such as Fox colors are well-studied. As the…
Minimum numbers of Dehn colors of knots and symmetric local biquandle cocycle invariants
Eri Matsudo, Kanako Oshiro, Gaishi Yamagishi
In this paper, we give a method to evaluate minimum numbers of Dehn colors for knots by using symmetric local biquandle cocycle invariants. We give answers to some questions arisin…
Minimum numbers of Dehn colors of knots and -palette graphs
Eri Matsudo, Kanako Oshiro, Gaishi Yamagishi
In this paper, we consider minimum numbers of colors of knots for Dehn colorings. In particular, we will show that for any odd prime number and any Dehn -colorable knot ,…
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…
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…
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…
Minimal coloring numbers on minimal diagrams of torus links
Kazuhiro Ichihara, Katsumi Ishikawa, Eri Matsudo
We determine the minimal number of colors for non-trivial -colorings on the standard minimal diagrams of -colorable torus links. Also included are complete…
Minimal coloring number on minimal diagrams for -colorable links
Kazuhiro Ichihara, Eri Matsudo
It was shown that any -colorable link has a diagram which admits a non-trivial -coloring with at most four colors. In this paper, we consider minimal number…
Minimal coloring number for -colorable links II
Eri Matsudo
The minimal coloring number of a -colorable link is the minimal number of colors for non-trivial -colorings on diagrams of the link. In this paper, we show…
Minimal coloring number for Z-colorable links
Kazuhiro Ichihara, Eri Matsudo
For a link with zero determinants, a Z-coloring is defined as a generalization of Fox coloring. We call a link having a diagram which admits a non-trivial Z-coloring a Z-colorable…
A lower bound on minimal number of colors for links
Kazuhiro Ichihara, Eri Matsudo
We show that the minimal number of colors for all effective -colorings of a link with non-zero determinant is at least .