Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bounds for the circuit size of partially homogeneous polynomials   In this paper we associate to each multivariate polynomial $f$ that is
homogeneous relative to a subset of its variables a series of polynomial
families $P_\lambda (f)$ of $m$-tuples of homogeneous polynomials of equal
degree such that the circuit size of any member in $P_\lambda (f)$ is bounded
from above by the circuit size of $f$. This provides a method for obtaining
lower bounds for the circuit size of $f$ by proving $(s,r)$-(weak) elusiveness
of the polynomial mapping associated with $P_\lambda (f)$. We discuss some
algebraic methods for proving the $(s,r)$-(weak) elusiveness. We also improve
estimates in the normal homogeneous-form of an arithmetic circuit obtained by
Raz in \cite{Raz2009} which results in better lower bounds for circuit size
(Lemma \ref{lem:cor38}, Remark \ref{rem:cor38}).
  Our methods yield non-trivial lower bound for the circuit size of several
classes of multivariate homogeneous polynomials (Corollary \ref{cor:412},
Example \ref{ex:bi}).

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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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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: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph