Shin Satoh

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

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…

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…

A note on Fox colorings of virtual tangles

Hurwitz equivalence in the universal dihedral quandle

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

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