Shin Satoh

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20242026

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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…

A note on Fox colorings of virtual tangles

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

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