Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Macdonald cumulants, $G$-inversion polynomials and $G$-parking functions   We prove a combinatorial formula for Macdonald cumulants which generalizes
the celebrated formula of Haglund for Macdonald polynomials. We provide several
applications of our formula. Firstly, it gives a new, constructive proof of a
strong factorization property of Macdonald polynomials proven recently by the
author of this paper. Moreover it proves that Macdonald cumulants are
$q,t$--positive in the monomial and in the fundamental quasisymmetric bases.
Furthermore, we use our formula to prove the recent higher-order Macdonald
positivity conjecture for the coefficients of the Schur polynomials indexed by
hooks. Our combinatorial formula relates Macdonald cumulants to the generating
function of $G$-parking functions, or equivalently to a certain specialization
of the Tutte polynomials.

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The categories of this paper are: bayes-an
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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: eess
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con