2019/11/17 by Denis Petrovich Ilyutko, Denis P. Ilyutko, Vassily Olegovich Manturov +3
Computer Science · Mathematics · #57M15 #57M25 #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M15 #msc:57M25 #msc:57M27 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1911.07843
16 pages, 15 figures
arxiv created 2019/11/17 · openalex publication_date 2019/11/17 · arxiv updated 2019/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [3] we constructed the parity-biquandle bracket valued in \em pictures (linear combinations of 4-valent graphs). We gave no example of classical links such that the parity-biquandle bracket of which is not trivial. In the present paper we slightly change the notation of the parity-biquandle bracket and give examples of knots and links having a non-trivial parity-biquandle bracket. As a result we get the minimality theorem. This is the first evidence that graphs (link shadows) appear as invariants of link diagrams instead of just polynomials groups and other tractable objects.