8 citations · 37 across the 10 of their papers we have counts for
13 papers · 1 filter
Any nontrivial knot projection with no triple chords has a monogon or a bigon
Noboru Ito, Yusuke Takimura
A generic immersion of a circle into a -sphere is often studied as a projection of a knot; it is called a knot projection. A chord diagram is a configuration of paired points on…
The tabulation of prime knot projections with their mirror images up to eight double points
Noboru Ito, Yusuke Takimura
This paper provides the complete table of prime knot projections with their mirror images, without redundancy, up to eight double points systematically thorough a finite procedure…
Thirty-two equivalence relations on knot projections
Noboru Ito, Yusuke Takimura
We consider 32 homotopy classifications of knot projections (images of generic immersions from a circle into a 2-sphere). These 32 equivalence relations are obtained based on which…
Strong and weak (1, 3) homotopies on knot Projections
Noboru Ito, Yusuke Takimura, Kouki Taniyama
Strong and weak (1, 3) homotopies are equivalence relations on knot projections, defined by the first flat Reidemeister move and each of two different types of the third flat Reide…
On a nontrivial knot projection under (1, 3) homotopy
Noboru Ito, Yusuke Takimura
In 2001, Östlund formulated the question: are Reidemeister moves of types 1 and 3 sufficient to describe a homotopy from any generic immersion of a circle in a two-dimensional plan…
Strong and weak (1, 2) homotopies on knot projections and new invariants
Noboru Ito, Yusuke Takimura
Every second flat Reidemeister move of knot projections can be decomposed into two types thorough an inverse or direct self-tangency modification, respectively called strong or wea…