1 citations · 2 across the 10 of their papers we have counts for
10 papers
A note on Fox colorings of virtual tangles
Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh +1
We study Fox colorings of tangle diagrams by or , where is an odd integer. For an -colored -string tangle diagram, the colors…
The intersection polynomials of a long virtual knot II: Two supporting genera and characterizations
Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh +1
We develop the study of the twelve intersection polynomials of long virtual knots, previously introduced in our preceding paper. We define two geometric invariants, the - and $2…
The intersection polynomials of a long virtual knot I: Definitions and properties
Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh +1
We introduce twelve polynomial invariants for long virtual knots, called intersection polynomials, extending and refining the three intersection polynomials for virtual knots. They…
Hurwitz equivalence in the universal dihedral quandle
Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh +1
We investigate the Hurwitz action of the -braid group on the -fold Cartesian product of the universal dihedral quandle. We introduce three computable invariants and prove tha…
Virtualized Delta, sharp, and pass moves for oriented virtual knots and links
Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh +1
We study virtualized Delta, sharp, and pass moves for oriented virtual links, and give necessary and sufficient conditions for two oriented virtual links to be related by the local…
Virtualized Delta moves for virtual knots and links
Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh +1
We introduce a local deformation called the virtualized -move for virtual knots and links. We prove that the virtualized -move is an unknotting operation for virtual knots. F…
The intersection polynomials of a virtual knot I: Definitions and calculations
Ryuji Higa, Takuji Nakamura, Yasutaka Nakanishi +1
We introduce three kinds of invariants of a virtual knot called the first, second, and third intersection polynomials. The definition is based on the intersection number of a pair…
Writhe polynomials and shell moves for virtual knots and links
Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh
The writhe polynomial is a fundamental invariant of an oriented virtual knot. We introduce a kind of local moves for oriented virtual knots called shell moves. The first aim of thi…
A note on coverings of virtual knots
Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh
For a virtual knot and an integer , the -covering is defined by using the indices of chords on a Gauss diagram of . In this paper, we prove that for an…
11-colored knot diagram with five colors
Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh
We prove that any -colorable knot is presented by an -colored diagram where exactly five colors of eleven are assigned to the arcs. The number five is the minimum for all n…