4 citations · 7 across the 8 of their papers we have counts for
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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 second Yang-Baxter homology for the Homflypt polynomial
Jozef H. Przytycki, Xiao Wang
In this article, we adjust the Yang-Baxter operators constructed by Jones for the HOMFLYPT polynomal. Then we compute the second homology for this family of Yang-Baxter operators.…
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…
On multiplying curves in the Kauffman bracket skein algebra of the thickened four-holed sphere
Rhea Palak Bakshi, Sujoy Mukherjee, Józef H. Przytycki +2
Based on the presentation of the Kauffman bracket skein module of the torus given by the third author in previous work, Charles D. Frohman and Răzvan Gelca established a complete d…
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…
Equivalence of two definitions of set-theoretic Yang-Baxter homology
Jozef H. Przytycki, Xiao Wang
In 2004, Carter, Elhamdadi and Saito defined a homology theory for set-theoretic Yang-Baxter operators(we will call it the "algebraic" version in this article). In 2012, Przytycki…