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arxiv: 1105.1264 · v2 · pith:GJHRF5IUnew · submitted 2011-05-06 · 🧮 math.GT

Bipartite knots

S. Duzhin , M. Shkolnikov This is my paper
classification 🧮 math.GT
keywords knotsansweringbipartiteconcerningconjecturediagramsexistencegive
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We give a solution to a part of Problem 1.60 in Kirby's list of open problems in topology thus answering in the positive the 1987 conjecture by J.Przytycki concerning the existence of knots without matched diagrams.

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  1. Analogue of Goeritz matrices for computation of bipartite HOMFLY-PT polynomials

    math.GT 2025-07 unverdicted novelty 6.0

    A modified Goeritz matrix is defined for bipartite link diagrams that reduces HOMFLY-PT computation for any N to matrix algebra.