7 papers · 1 filter
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 - and -polynomials of a long virtual knot
Shin Satoh, Kodai Wada
We introduce two polynomial invariants and of a long virtual knot , which generalize the degree-two finite type invariants and of Gouss…
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…