Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An algebraic independence result related to a conjecture of Dixmier on
  binary form invariants   In order to better understand the structure of classical rings of invariants
for binary forms, Dixmier proposed, as a conjectural homogeneous system of
parameters, an explicit collection of invariants previously studied by Hilbert.
We generalize Dixmier's collection and show that a particular subfamily is
algebraically independent. Our proof relies on showing certain alternating sums
of products of binomial coefficients are nonzero. Along the way we provide a
very elementary proof \`a la Racah, namely, only using the Chu-Vandermonde
Theorem, for Dixon's Summation Theorem. We also provide explicit computations
of invariants, for the binary octavic, which can serve as ideal introductory
examples to Gordan's 1868 method in classical invariant theory.

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The categories of this paper are: comp-gas
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th