Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Square numbers, spanning trees and invariants of achiral knots   We give constructions to realize an odd number, which is representable as sum
of two squares, as determinant of an achiral knot, thus proving that these are
exactly the numbers occurring as such determinants. Later we study which
numbers occur as determinants of prime alternating achiral knots, and obtain a
complete result for perfect squares. Using the checkerboard coloring, then an
application is given to the number of spanning trees in planar self-dual
graphs. Another application are some enumeration results on achiral rational
knots. Finally, we describe the leading coefficients of the Alexander and skein
polynomial of alternating achiral knots.

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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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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: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th