Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Number of orbits of Discrete Interval Exchanges   A new recursive function on discrete interval exchange transformation
associated to a composition of length $r$, and the permutation $\sigma(i) = r
-i +1$ is defined. Acting on composition $c$, this recursive function counts
the number of orbits of the discrete interval exchange transformation
associated to the composition $c$. Moreover, minimal discrete interval
exchanges transformation i.e. the ones having only one orbit, are reduced to
the composition which label the root of the Raney tree. Therefore, we describe
a generalization of the Raney tree using our recursive function.

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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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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: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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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: comp-gas
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The categories of this paper are: cs