Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The inverse Kazhdan-Lusztig polynomial of a matroid   In analogy with the classical Kazhdan-Lusztig polynomials for Coxeter groups,
Elias, Proudfoot and Wakefield introduced the concept of Kazhdan-Lusztig
polynomials for matroids. It is known that both the classical Kazhdan-Lusztig
polynomials and the matroid Kazhdan-Lusztig polynomials can be considered as
special cases of the Kazhdan-Lusztig-Stanley polynomials for locally finite
posets. In the framework of Kazhdan-Lusztig-Stanley polynomials, we study the
inverse of Kazhdan-Lusztig-Stanley functions and define the inverse
Kazhdan-Lusztig polynomials for matroids. We also compute these polynomials for
boolean matroids and uniform matroids. As an unexpected application of the
inverse Kazhdan-Lusztig polynomials, we obtain a new formula to compute the
Kazhdan-Lusztig polynomials for uniform matroids. Similar to the
Kazhdan-Lusztig polynomial of a matroid, we conjecture that the coefficients of
its inverse Kazhdan-Lusztig polynomial are nonnegative and log-concave.

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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol