Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Note on the number of balanced independent sets in the Hamming cube   Let $Q_d$ be the $d$-dimensional Hamming cube and $N=|V(Q_d)|=2^d$. An
independent set $I$ in $Q_d$ is called balanced if $I$ contains the same number
of even and odd vertices. We show that the logarithm of the number of balanced
independent sets in $Q_d$ is \[(1-\Theta(1/\sqrt d))N/2.\] The key ingredient
of the proof is an improved version of "Sapozhenko's graph container lemma."

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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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: quant-ph
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The categories of this paper are: hep-ex