4 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…
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…
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…