Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sum--of--squares results for polynomials related to the
  Bessis--Moussa--Villani conjecture   We show that the polynomial S_{m,k}(A,B), that is the sum of all words in
noncommuting variables A and B having length m and exactly k letters equal to
B, is not equal to a sum of commutators and Hermitian squares in the algebra
R<X,Y> where X^2=A and Y^2=B, for all even values of m and k with 6 <= k <=
m-10, and also for (m,k)=(12,6). This leaves only the case (m,k)=(16,8) open.
This topic is of interest in connection with the Lieb--Seiringer formulation of
the Bessis--Moussa--Villani conjecture, which asks whether the trace of
S_{m,k}(A,B)) is nonnegative for all positive semidefinite matrices A and B.
These results eliminate the possibility of using "descent + sum-of-squares" to
prove the BMV conjecture.
  We also show that S_{m,4}(A,B) is equal to a sum of commutators and Hermitian
squares in R<A,B> when m is even and not a multiple of 4, which implies that
the trace of S_{m,4}(A,B) is nonnegative for all Hermitian matrices A and B,
for these values of m.

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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con