6 citations · 16 across the 20 of their papers we have counts for
22 papers
Boolean algebra on region crossing change and an inequality of the region unknotting number
Dawan Chumpungam, Ayaka Shimizu
Using Boolean algebra, we discuss the region unknotting number of a knot, and show that the region unknotting number is less than or equal to (c+1)/2 for any knot with crossing num…
Lower bounds for the warping degree of a knot projection
Atsushi Ohya, Ayaka Shimizu
The warping degree of an oriented knot diagram is the minimal number of crossings which we meet as an under-crossing first when we travel along the diagram from a fixed point. The…
Unknottability of spatial graphs by region crossing changes
Yukari Funakoshi, Kenta Noguchi, Ayaka Shimizu
A region crossing change is a local transformation on spatial graph diagrams switching the over/under relations at all the crossings on the boundary of a region. In this paper, we…
Prime alternating knots of minimal warping degree two
Ayaka Shimizu
The warping degree of an oriented knot diagram is the minimal number of crossing changes which are required to obtain a monotone knot diagram from the diagram. The minimal warping…
Region crossing change on spatial theta-curves
Ayaka Shimizu, Rinno Takahashi
A region crossing change at a region of a spatial-graph diagram is a transformation changing every crossing on the boundary of the region. In this paper, it is shown that every spa…
A note on the cross-index of a complete graph based on a linear tree
Yusuke Gokan, Hayato Katsumata, Katsuya Nakajima +2
In this paper it is shown that a complete graph with vertices has an optimal diagram, i.e., a diagram whose crossing number equals the value of Guy's formula, with a free maxim…
On the warping sum of knots
Slavik Jablan, Ayaka Shimizu
The warping sum of a knot is the minimal value of the sum of the warping degrees of a minimal diagram of with both orientations. In this paper, knots with $e(K)…
A note on unavoidable sets for a spherical curve of reductivity four
Kenji Kashiwabara, Ayaka Shimizu
The reductivity of a spherical curve is the minimal number of a local transformation called an inverse-half-twisted splice required to obtain a reducible spherical curve from the s…
Up-down colorings of virtual-link diagrams and the necessity of Reidemeister moves of type II
Kanako Oshiro, Ayaka Shimizu, Yoshiro Yaguchi
We introduce an up-down coloring of a virtual-link diagram. The colorabilities give a lower bound of the minimum number of Reidemeister moves of type II which are needed between tw…
Biquandle Virtual Brackets
Sam Nelson, Kanako Oshiro, Ayaka Shimizu +1
We introduce an infinite family of quantum enhancements of the biquandle counting invariant we call biquandle virtual brackets. Defined in terms of skein invariants of biquandle co…
Axis systems of link projections
Kirara Horiguchi, Ayaka Shimizu, Ryohei Watanabe +1
An axis of a link projection is a closed curve which lies symmetrically on each region of the link projection. In this paper we define axis systems of link projections and characte…
The reductivity of spherical curves Part II: 4-gons
Yui Onoda, Ayaka Shimizu
The reductivity of a spherical curve represents how reduced the spherical curve is. It is unknown if there exists a spherical curve whose reductivity is four. In this paper we give…
The rank of a warping matrix
Taira Akiyama, Ayaka Shimizu, Ryohei Watanabe
The warping matrix has been defined for knot projections and knot diagrams by using warping degrees. In particular, the warping matrix of a knot diagram represents the knot diagram…
The warping matrix of a knot diagram
Ayaka Shimizu
We introduce the warping matrix which is a new description of oriented knots from a viewpoint of warping degree.
The reductivity of spherical curves
Ayaka Shimizu
We show that we can obtain a reducible spherical curve from any non-trivial spherical curve by four or less inverse-half-twisted splices, i.e., the reductivity, which represents ho…
The half-twisted splice operation on reduced knot projections
Noboru Ito, Ayaka Shimizu
We show that any nontrivial reduced knot projection can be obtained from a trefoil projection by a finite sequence of half-twisted splice operations and their inverses such that th…
Quantization of the crossing number of a knot diagram
Akio Kawauchi, Ayaka Shimizu
We introduce the warping crossing polynomial of an oriented knot diagram by using the warping degrees of crossing points of the diagram. Given a closed transversely intersected pla…
The warping polynomial of a knot diagram
Ayaka Shimizu
We introduce the warping polynomial of an oriented knot diagram. In this paper, we characterize the warping polynomial, and define the span of a knot to be the minimal span of the…
Region crossing change is an unknotting operation
Ayaka Shimizu
Region crossing change is a local transformation on a knot or link diagram. We show that a region crossing change on a knot diagram is an unknotting operation, and we define the re…
The complete splitting number of a lassoed link
Ayaka Shimizu
In this paper, we define a lassoing on a link, a local addition of a trivial knot to a link. Let K be an s-component link with the Conway polynomial non-zero. Let L be a link which…
The warping degree of a link diagram
Ayaka Shimizu
For an oriented link diagram D, the warping degree d(D) is the smallest number of crossing changes which are needed to obtain a monotone diagram from D. We show that d(D)+d(-D)+sr(…
The warping degree of a knot diagram
Ayaka Shimizu
For an oriented knot diagram D, the warping degree d(D) is the smallest number of crossing changes which are needed to obtain the monotone diagram from D in the usual way. We show…