Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Number System of the Permutations Generated by Cyclic Shift   A number system coding for the permutations generated by cyclic shift is
described. The system allows to find the rank of a permutation given how it has
been generated, and to determine a permutation given its rank. It defines a
code describing the symmetry properties of the set of permutations generated by
cyclic shift. This code is conjectured to be a combinatorial Gray code listing
the set of permutations: this corresponds to an Hamiltonian path of minimal
weight in an appropriate regular digraph.

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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: cond-mat