4 papers
Characterization of non-self OU sequences of two-component link diagrams
Naoki Sakata, Ayaka Shimizu, Koya Shimokawa
A non-self OU sequence is a cyclic sequence of crossing information of non-self crossings that is obtained by traversing a knot component of an oriented link diagram. In this paper…
The OU number and Reidemeister moves of type III for link diagrams
Naoki Sakata, Ayaka Shimizu, Koya Shimokawa
We introduce the non-self OU sequence and the OU number for link diagrams. Using these, we give a lower bound for the number of necessary Reidemeister moves of type III between two…
A note on the unknotting number and the region unknotting number of weaving knots
Ayaka Shimizu, Amrendra Gill, Sahil Joshi
A weaving knot is an alternating knot whose minimal diagram is a closed braid of a lattice-like pattern. In this paper, the warping degree of a braid diagram is defined, and upper…
Isolated regions of a link projection
Tumpa Mahato, Ayaka Shimizu
A set of regions of a link projection is said to be isolated if any pair of regions in the set share no crossings. The isolate-region number of a link projection is the maximum val…