8 citations · 11 across the 15 of their papers we have counts for
15 papers
The linear minimal 4-chart with three crossings
Teruo Nagase, Akiko Shima
Charts are oriented labeled graphs in a disk. Any simple surface braid (2-dimensional braid) can be described by using a chart. Also, a chart represents an oriented closed surface…
Properties of minimal charts and their applications X: charts of type
Teruo Nagase, Akiko Shima
Charts are oriented labeled graphs in a disk. Any simple surface braid (2-dimensional braid) can be described by using a chart. Also, a chart represents an oriented closed surface…
Properties of minimal charts and their applications XI: no minimal charts with exactly seven white vertices
Teruo Nagase, Akiko Shima
Charts are oriented labeled graphs in a disk. Any simple surface braid (2-dimensional braid) can be described by using a chart. Also, a chart represents an oriented closed surface…
Distinguishing surface-links with 4-charts with 2 crossings and 8 black vertices
Teruo Nagase, Akiko Shima
Charts are oriented labeled graphs in a disk. Any simple surface braid (2-dimensional braid) can be described by using a chart. Also, a chart represents an oriented closed surface…
Properties of minimal charts and their applications IX: charts of type
Teruo Nagase, Akiko Shima
Charts are oriented labeled graphs in a disk. Any simple surface braid (2-dimensonal braid) can be described by using a chart. Also, a chart represents an oriented closed surface e…
Properties of minimal charts and their applications VIII: charts of type
Teruo Nagase, Akiko Shima
Let be a chart, and we denote by the union of all the edges of label . A chart is of type if there exists a label such that , $w(Γ_m\capΓ_{m+1})=…
Properties of minimal charts and their applications VII: charts of type
Teruo Nagase, Akiko Shima
Let be a chart, and we denote by the union of all the edges of label . A chart is of type if there exists a label such that , $w(Γ_m\capΓ_{m+…
Properties of minimal charts and their applications VI: the graph in a chart of type
Teruo Nagase, Akiko Shima
Let be a chart, and we denote by the union of all the edges of label . A chart is of type if , , …
Properties of minimal charts and their applications V: charts of type
Teruo Nagase, Akiko Shima
Let be a chart, and we denote by the union of all the edges of label . A chart is of type if there exists a label such that , $w(Γ_m\capΓ_{m+…
The structure of a minimal -chart with two crossings II: Neighbourhoods of
Teruo Nagase, Akiko Shima
Given a 2-crossing minimal chart , a minimal chart with two crossings, set there exists an edge of label containing a white vertex, and the…
The structure of a minimal -chart with two crossings I: Complementary domains of
Teruo Nagase, Akiko Shima
This is the first step of the two steps to enumerate the minimal charts with two crossings. For a label of a chart we denote by the union of all the edges of label $m…
Minimal charts of type (3,3)
Teruo Nagase, Akiko Shima
Let be a chart. For each label , we denote by the "subgraph" of consisting of all the edges of label and their vertices. Let be a minimal chart of type $(m…
Separating a chart
Teruo Nagase, Akiko Shima
In this paper, we shall show a condition for that a chart is C-move equivalent to the product of two charts, the union of two charts and which are contained in disks…
Properties of minimal charts and their applications IV: Loops
Teruo Nagase, Akiko Shima
We investigate minimal charts with loops, a simple closed curve consisting of edges of label containing exactly one white vertex. We shall show that there does not exist any lo…
Minimal Charts
Teruo Nagase, Akiko Shima
In this paper, we give definitions of three kinds of minimal charts, and we investigate properties of minimal charts and establish fundamental theorems characterizing minimal chart…