Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twist Lattices and the Jones-Kauffman Polynomial for Long Virtual Knots   In this paper, we investigate twist sequences for Kauffman finite-type
invariants and Goussarov-Polyak-Viro finite-type invariants. It is shown that
one obtains a Kauffman or GPV type of degree $\le n$ if and only if an
invariant is a polynomial of degree $\le n$ on every twist lattice of the right
form. The main result of this paper is an application of this technique to the
coefficients of the Jones-Kauffman polynomial. It is shown that the Kauffman
finite-type invariants obtained from these coefficients are not GPV finite-type
invariants of any degree by explicitly showing they can never be polynomials.
This generalizes a result of Kauffman, where it is known for degree $k=2$.

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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat