Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Ehrhart Polynomial of Schubert Matroids   In this paper, we give a formula for the number of lattice points in the
dilations of Schubert matroid polytopes. As applications, we obtain the Ehrhart
polynomials of uniform and minimal matroids as simple special cases, and give a
recursive formula for the Ehrhart polynomials of $(a,b)$-Catalan matroids.
Ferroni showed that uniform and minimal matroids are Ehrhart positive. We show
that all sparse paving Schubert matroids are Ehrhart positive and their Ehrhart
polynomials are coefficient-wisely bounded by those of minimal and uniform
matroids. This confirms a conjecture of Ferroni for the case of sparse paving
Schubert matroids. Furthermore, we express the Ehrhart polynomials of three
families of Schubert matroids as positive combinations of the Ehrhart
polynomials of uniform matroids, yielding Ehrhart positivity of these Schubert
matroids.

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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat