Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some remarks on the joint distribution of descents and inverse descents   We study the joint distribution of descents and inverse descents over the set
of permutations of n letters. Gessel conjectured that the two-variable
generating function of this distribution can be expanded in a given basis with
nonnegative integer coefficients. We investigate the action of the Eulerian
operators that give the recurrence for these generating functions. As a result
we devise a recurrence for the coefficients but are unable to settle the
conjecture. We examine generalizations of the conjecture and obtain a type B
analog of the recurrence satisfied by the two-variable generating function. We
also exhibit some connections to cyclic descents and cyclic inverse descents.
Finally, we propose a combinatorial model in terms of statistics on inversion
sequences.

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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: acc-phys