Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fair representation in the intersection of two matroids   For a simplicial complex ${\mathcal C}$ denote by $\beta({\mathcal C})$ the
minimal number of edges from ${\mathcal C}$ needed to cover the ground set. If
${\mathcal C}$ is a matroid then for every partition $A_1, \ldots, A_m$ of the
ground set there exists a set $S \in {\mathcal C}$ meeting each $A_i$ in at
least $\frac{|A_i|}{\beta({\mathcal C})}$ elements. We conjecture that a
slightly weaker result is true for the intersections of two matroids: if
${\mathcal D}={\mathcal P} \cap {\mathcal Q}$, where ${\mathcal P},{\mathcal
Q}$ are matroids on the same ground set $V$ and $\beta({\mathcal P}),
\beta({\mathcal P}) \le k$, then for every partition $A_1, \ldots, A_m$ of the
ground set there exists a set $S \in {\mathcal D}$ meeting each $A_i$ in at
least $(\frac{1}{k}-\frac{1}{|V|})|A_i|-1$ elements. We prove this for a
partition into two sets.

21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
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The categories of this paper are: eess
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas