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It is well-known that a knot is Fox $n$-colorable for a prime $n$ if and only if the knot group admits a surjective homomorphism to the dihedral group of degree $n$. However, this is not the case for links with two or more components. In this paper,
Externí odkaz:
http://arxiv.org/abs/2302.13706
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 Goeritz matrix (precisely, unreduced Goeritz matrix called in his paper) a
Externí odkaz:
http://arxiv.org/abs/2206.01983
Autor:
Ichihara, Kazuhiro, Matsudo, Eri
We consider the number of colors for the colorings of links by the symmetric group $S_3$ of degree $3$. For knots, such a coloring corresponds to a Fox 3-coloring, and thus the number of colors must be 1 or 3. However, for links, there are colorings
Externí odkaz:
http://arxiv.org/abs/2112.02515
We determine the minimal number of colors for non-trivial $\mathbb{Z}$-colorings on the standard minimal diagrams of $\mathbb{Z}$-colorable torus links. Also included are complete classifications of such $\mathbb{Z}$-colorings and of such $\mathbb{Z}
Externí odkaz:
http://arxiv.org/abs/1908.00857
Autor:
Ichihara, Kazuhiro, Matsudo, Eri
It was shown that any $\mathbb{Z}$-colorable link has a diagram which admits a non-trivial $\mathbb{Z}$-coloring with at most four colors. In this paper, we consider minimal numbers of colors for non-trivial $\mathbb{Z}$-colorings on minimal diagrams
Externí odkaz:
http://arxiv.org/abs/1710.03919
Autor:
Matsudo, Eri
The minimal coloring number of a $\mathbb{Z}$-colorable link is the minimal number of colors for non-trivial $\mathbb{Z}$-colorings on diagrams of the link. In this paper, we show that the minimal coloring number of any non-splittable $\mathbb{Z}$-co
Externí odkaz:
http://arxiv.org/abs/1705.07567
Autor:
Ichihara, Kazuhiro, Matsudo, Eri
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 link. The minimal coloring number of a Z-colorable link is the minimal
Externí odkaz:
http://arxiv.org/abs/1605.08127
Autor:
Ichihara, Kazuhiro, Matsudo, Eri
We show that the minimal number of colors for all effective $n$-colorings of a link with non-zero determinant is at least $1+\log_2 n$.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/1507.04088
Publikováno v:
研究紀要. 58(185):194
In 1933, L.Goeritz introduced an integral matrix associated to a knot diagram, which is now called a Goeritz matrix, and proved that the ab-solute value of the determinant of the matrix gives an invariant of a knot. Recently, it was shown that the Go
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=jairo_______::038890599f7cfb228d3f50fb82436731
https://repository.nihon-u.ac.jp/xmlui/handle/11263/2319
https://repository.nihon-u.ac.jp/xmlui/handle/11263/2319
Autor:
Ichihara, Kazuhiro, Matsudo, Eri
Publikováno v:
数理解析研究所講究録. 2099:1-12
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=jairo_______::5b7c03d0d563baa17e8c1ae025cf6858
http://hdl.handle.net/2433/251776
http://hdl.handle.net/2433/251776