6 citations · 16 across the 20 of their papers we have counts for
4 papers · 1 filter
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…