Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Approximate Degree of Bipartite Perfect Matching   The approximate degree of a Boolean function is the least degree of a real
multilinear polynomial approximating it in the $\ell_\infty$-norm over the
Boolean hypercube. We show that the approximate degree of the Bipartite Perfect
Matching function, which is the indicator over all bipartite graphs having a
perfect matching, is $\widetilde{\Theta}(n^{3/2})$.
  The upper bound is obtained by fully characterizing the unique multilinear
polynomial representing the Boolean dual of the perfect matching function, over
the reals. Crucially, we show that this polynomial has very small $\ell_1$-norm
-- only exponential in $\Theta(n \log n)$. The lower bound follows by bounding
the spectral sensitivity of the perfect matching function, which is the
spectral radius of its cut-graph on the hypercube \cite{aaronson2020degree,
huang2019induced}. We show that the spectral sensitivity of perfect matching is
exactly $\Theta(n^{3/2})$.

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The categories of this paper are: comp-gas
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio