2018/05/20 by Zhiyun Cheng, Cheng, Zhiyun
Computer Science · Engineering · Mathematics · #57M25 #57M27 #Advanced Combinatorial Mathematics #Combinatorics #Computational Geometry and Mesh Generation #Crossing number (knot theory) #Engineering #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Mathematical analysis #Mathematics #Physics #Polynomial #Twist #Writhe #math.GT #msc:57M25 #msc:57M27
paper · pdf · doi:10.48550/arxiv.1805.07704
The main result of this paper has been obtained by S. Satoh and K. Taniguchi in "The writhes of a virtual knot", Fundamenta Mathematicae 225 (2014), no. 1,327--342
openalex publication_date 2018/05/20 · arxiv created 2018/05/24 · arxiv updated 2018/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we give a new lower bound on the virtual crossing number via the writhe polynomial, which refines a result of B. Mellor. The proof is based on a new interpretation of the writhe polynomial. The characterization of the writhe polynomial is also discussed.