3 citations · 3 across the 8 of their papers we have counts for
9 papers
Computations of parabolic character schemes of knots
Yunhi Cho, Hyuk Kim, Seonhwa Kim +1
We compute parabolic -character schemes of knots using the parabolic quandle. To this end, we introduce sign-refined arc-colorings and show that their si…
Rigidity of nonconvex polyhedra with respect to edge lengths and dihedral angles
Yunhi Cho, Seonhwa Kim
We prove that every three-dimensional polyhedron is uniquely determined by its dihedral angles and edge lengths, even if nonconvex or self-intersecting, under two plausible suffici…
Parabolic representations and generalized Riley polynomials
Yunhi Cho, Hyuk Kim, Seonhwa Kim +1
We generalize R. Riley's study about parabolic representations of two bridge knot groups to the general knots in . We utilize the parabolic quandle method for general knot dia…
Partially abelian representations of knot groups
Yunhi Cho, Seokbeom Yoon
A knot complement admits a pseudo-hyperbolic structure by solving Thurston's gluing equations for an octahedral decomposition. It is known that a solution to these equations can be…
A classification of polyhedral graph by combinatorially rigid vertices
Seonhwa Kim, Yunhi Cho
When the number of non-triangular faces adjacent to a vertex is less than or equal to three, the vertex will be called (\emph{combinatorially}) \emph{rigid}. We study the n…
Volume of Hypercubes Clipped by Hyperplanes and Combinatorial Identities
Yunhi Cho, Seonhwa Kim
There is an elegant expression for the volume of hypercube clipped by a single hyperplane. In the article the formula is generalized to the case of more than one hyperpla…
Trigonometry in extended hyperbolic space and extended de Sitter space
Yunhi Cho
We study the hyperbolic cosine and sine laws in the extended hyperbolic space which contains hyperbolic space as a subset and is an analytic continuation of the hyperbolic space. A…
Volume of -boundary domain in extended hyperbolic space
Yunhi Cho, Hyuk Kim
We consider the projectivization of Minkowski space with the analytic continuation of the hyperbolic metric and call this an extended hyperbolic space. We can measure the volume of…
The analytic continuation of hyperbolic space
Yunhi Cho, Hyuk Kim
We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter space as subspaces and which is obtained as an analytic continuation of the hyper…