Analogue of Goeritz matrices for computation of bipartite HOMFLY-PT polynomials
Analogue of Goeritz matrices for computation of bipartite HOMFLY-PT polynomials
The Goeritz matrix is an alternative to the Kauffman bracket and, in addition, makes it possible to calculate the Jones polynomial faster with some minimal choice of a checkerboard surface of a link diagram. We introduce a modification of the Goeritz method that generalizes the Goeritz matrix for computing the HOMFLY-PT polynomials for any $N$ in the special case of bipartite links. Our method reduces to purely algebraic operations on matrices, and therefore, it can be easily implemented as a computer program. Bipartite links form a rather large family including a special class of Montesinos links constructed from the so-called rational tangles. We demonstrate how to obtain a bipartite diagram of such links and calculate the corresponding HOMFLY-PT polynomials using our developed generalized Goeritz method.
A. Anokhina、D. Korzun、E. Lanina、A. Morozov
数学
A. Anokhina,D. Korzun,E. Lanina,A. Morozov.Analogue of Goeritz matrices for computation of bipartite HOMFLY-PT polynomials[EB/OL].(2025-07-03)[2025-07-16].https://arxiv.org/abs/2507.03116.点此复制
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