2024/02/22 by Mohamed Elhamdadi, Elhamdadi, Mohamed, Dipali Swain +1 · 1 citation
Computer Science · Mathematics · #57-K-12 #Advanced Algebra and Logic #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2402.14661
openalex publication_date 2024/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use idempotents in quandle rings in combination with the state sum invariants of knots to distinguish all of the 12965 prime oriented knots up to 13 crossings using only 21 connected quandles and three quandles made of idempotents in quandle rings. We also distinguish all knots up to 13 crossings from their mirror images using the same 24 quandles. Furthermore, we distinguish all of the 2977 prime oriented knots up to 12 crossings using only 10 connected quandles and three quandles made of idempotents in quandle rings. This improves a result in [Quandle colorings of knots and applications, J. Knot Theory Ramifications 23 (2014), no. 6, 1450035]. Our computations are achieved with the help of Python and Maple softwares.