15 citations · 20 across the 12 of their papers we have counts for
12 papers
The intersection polynomials of a virtual knot I: Definitions and calculations
Ryuji Higa, Takuji Nakamura, Yasutaka Nakanishi +1
We introduce three kinds of invariants of a virtual knot called the first, second, and third intersection polynomials. The definition is based on the intersection number of a pair…
Classification of -component virtual links up to -moves
Jean-Baptiste Meilhan, Shin Satoh, Kodai Wada
The -move is a local move generated by forbidden moves in virtual knot theory. This move was introduced by Taniguchi and the second author, who showed that it characterizes the…
Writhe polynomials and shell moves for virtual knots and links
Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh
The writhe polynomial is a fundamental invariant of an oriented virtual knot. We introduce a kind of local moves for oriented virtual knots called shell moves. The first aim of thi…
A note on coverings of virtual knots
Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh
For a virtual knot and an integer , the -covering is defined by using the indices of chords on a Gauss diagram of . In this paper, we prove that for an…
Crossing changes, Delta moves, and sharp moves on welded knots
Shin Satoh
We prove that the crossing changes, Delta moves, and sharp moves are unknotting operations on welded knots.
11-colored knot diagram with five colors
Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh
We prove that any -colorable knot is presented by an -colored diagram where exactly five colors of eleven are assigned to the arcs. The number five is the minimum for all n…