4 citations · 7 across the 11 of their papers we have counts for
14 papers
Effective data reduction algorithm for topological data analysis
Seonmi Choi, Jinseok Oh, Jeong Rye Park +2
One of the most interesting tools that have recently entered the data science toolbox is topological data analysis (TDA). With the explosion of available data sizes and dimensions,…
Set-theoretic Yang-Baxter cohomology of cyclic biquandles
Minyi Liang, Xiao Wang, Seung Yeop Yang
We completely determine the free parts of the set-theoretic Yang-Baxter (co)homology groups of finite cyclic biquandles, along with fully computing the torsion subgroups of their 1…
The geometric realization of a normalized set-theoretic Yang-Baxter homology of biquandles
Xiao Wang, Seung Yeop Yang
Biracks and biquandles, which are useful for studying the knot theory, are special families of solutions of the set-theoretic Yang-Baxter equation. A homology theory for the set-th…
Enumeration of racks and quandles up to isomorphism
Petr Vojtěchovský, Seung Yeop Yang
Racks and quandles are prominent set-theoretical solutions of the Yang-Baxter equation. We enumerate racks and quandles of orders up to isomorphism, improving upon the pr…
Set-theoretic Yang-Baxter (co)homology theory of involutive non-degenerate solutions
Józef H. Przytycki, Petr Vojtěchovský, Seung Yeop Yang
W. Rump showed that there exists a one-to-one correspondence between involutive right non-degenerate solutions of the Yang-Baxter equation and Rump right quasigroups. J. S. Carter,…
Structure for -Metric Spaces and Related Fixed Point Theorems
Hayoung Choi, Sejong Kim, Seung Yeop Yang
In this paper, we propose a generalized notion of a distance function, called a -metric. The -metric with degree is a distance of points, generalizing the ordinary…
A prismatic classifying space
J. Scott Carter, Victoria Lebed, Seung Yeop Yang
A qualgebra is a set having two binary operations that satisfy compatibility conditions which are modeled upon a group under conjugation and multiplication. We develop a homolo…
Rooted trees with the same plucking polynomial
Zhiyun Cheng, Sujoy Mukherjee, Jozef Przytycki +2
In this paper we give a sufficient and necessary condition for two rooted trees with the same plucking polynomial. Furthermore, we give a criteria for a sequence of non-negative in…
Search for torsion in Khovanov homology
Sujoy Mukherjee, Józef H. Przytycki, Marithania Silvero +2
In the Khovanov homology of links, presence of -torsion is a very common phenomenon. Finite number of examples of knots with -torsion for were als…
Extended quandle spaces and shadow homotopy invariants of classical links
Seung Yeop Yang
In 1993, Fenn, Rourke and Sanderson introduced rack spaces and rack homotopy invariants, and modifications to quandle spaces and quandle homotopy invariants were introduced by Nosa…
Strict unimodality of q-polynomials of rooted trees
Zhiyun Cheng, Sujoy Mukherjee, Jozef H. Przytycki +2
We classify rooted trees which have strictly unimodal q-polynomials (plucking polynomial). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize res…
Annihilation of torsion in homology of finite -AQ quandles
Józef H. Przytycki, Seung Yeop Yang
It is a classical result in reduced homology of finite groups that the order of a group annihilates its homology. Similarly, we have proved that the torsion subgroup of rack and qu…
Twist Spinning Knotted Trivalent Graphs
J. Scott Carter, Seung Yeop Yang
In 1965, E. C. Zeeman proved that the (+/-)-twist spin of any knotted sphere in (n-1)-space is unknotted in the n-sphere. In 1991, Y. Marumoto and Y. Nakanishi gave an alternate pr…
The torsion of a finite quasigroup quandle is annihilated by its order
Jozef H. Przytycki, Seung Yeop Yang
We prove that if Q is a finite quasigroup quandle, then |Q| annihilates the torsion of its homology. It is a classical result in reduced homology of finite groups that the order of…