Shin Satoh

activity

20242026

collaborators

5 papers

math.GT2026

A note on Fox colorings of virtual tangles

Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh +1

We study Fox colorings of tangle diagrams by $R = Z$ or $Z / p Z$ , where $p \geq 3$ is an odd integer. For an $R$ -colored $m$ -string tangle diagram, the colors…

math.GT2026

The $V_{1}$ - and $V_{2}$ -polynomials of a long virtual knot

Shin Satoh, Kodai Wada

We introduce two polynomial invariants $V_{1} (K; t)$ and $V_{2} (K; t)$ of a long virtual knot $K$ , which generalize the degree-two finite type invariants $v_{2, 1}$ and $v_{2, 2}$ of Gouss…

math.GT2025

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 $1$ - and $2…

math.GT2025

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…

math.GT2024

Hurwitz equivalence in the universal dihedral quandle

Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh +1

We investigate the Hurwitz action of the $m$ -braid group on the $m$ -fold Cartesian product of the universal dihedral quandle. We introduce three computable invariants and prove tha…

A note on Fox colorings of virtual tangles

The V1​- and V2​-polynomials of a long virtual knot

The intersection polynomials of a long virtual knot II: Two supporting genera and characterizations

The intersection polynomials of a long virtual knot I: Definitions and properties

Hurwitz equivalence in the universal dihedral quandle

The $V_{1}$ - and $V_{2}$ -polynomials of a long virtual knot