3 citations · 6 across the 12 of their papers we have counts for
12 papers
Mosaics for immersed surface-links
Seonmi Choi, Jieon Kim
The concept of a knot mosaic was introduced by Lomonaco and Kauffman as a means to construct a quantum knot system. The mosaic number of a given knot is defined as the minimum…
Entropic Niebrzydowski Tribrackets
Jieon Kim, Sam Nelson
We introduce the notion of entropic Niebrzydowski tribrackets or just entropic tribrackets, analogous to entropic (also known as abelian or medial ) quandles and biquandles. We sho…
Quandle Coloring Quivers of Surface-Links
Jieon Kim, Sam Nelson, Minju Seo
Quandle coloring quivers are directed graph-valued invariants of oriented knots and links, defined using a choice of finite quandle and set of endom…
Psybrackets, Pseudoknots and Singular Knots
Suhyeon Jeong, Jieon Kim, Sam Nelson
We introduce algebraic structures known as psybrackets and use them to define invariants of pseudoknots and singular knots and links. Psybrackets are Niebrzydowski tribrackets with…
Cocycles of -Alexander biquandles and -Alexander multiple conjugation biquandles
Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada +3
Biquandles and multiple conjugation biquandles are algebras which are related to links and handlebody-links in -space. Cocycles of them can be used to construct state-sum type i…
Biquandle cohomology and state-sum invariants of links and surface-links
Seiichi Kamada, Akio Kawauchi, Jieon Kim +1
In this paper, we discuss the (co)homology theory of biquandles, derived biquandle cocycle invariants for oriented surface-links using broken surface diagrams and how to compute th…
Biquandle (co)homology and handlebody-links
Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada +3
In this paper, we introduce the (co)homology group of a multiple conjugation biquandle. It is the (co)homology group of the prismatic chain complex, which is related to the homolog…
Presentation of immersed surface-links by marked graph diagrams
Seiichi Kamada, Akio Kawauchi, Jieon Kim +1
It is well known that surface-links in 4-space can be presented by diagrams on the plane of 4-valent spatial graphs with makers on the vertices, called marked graph diagrams. In th…
Biquasile Colorings of Oriented Surface-Links
Jieon Kim, Sam Nelson
We introduce colorings of oriented surface-links by biquasiles using marked graph diagrams. We use these colorings to define counting invariants and Boltzmann enhancements of the b…
A multiple conjugation biquandle and handlebody-links
Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada +3
We introduce a multiple conjugation biquandle, and show that it is the universal algebra to define a semi-arc coloring invariant for handlebody-links. A multiple conjugation biquan…
Computations of quandle cocyle invariants of surface-links using marked graph diagrams
Seiichi Kamada, Jieon Kim, Sang Youl Lee
By using the cohomology theory of quandles, quandle cocycle invariants and shadow quandle cocycle invariants are defined for oriented links and surface-links via broken surface dia…
On generating sets of Yoshikawa moves for marked graph diagrams of surface-links
Jieon Kim, Yewon Joung, Sang Youl Lee
A marked graph diagram is a link diagram possibly with marked -valent vertices. S. J. Lomonaco, Jr. and K. Yoshikawa introduced a method of representing surface-links by marked…