Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cubic Harmonics and Bernoulli Numbers   The functions satisfying the mean value property for an n-dimensional cube
are determined explicitly. This problem is related to invariant theory for a
finite reflection group, especially to a system of invariant differential
equations. Solving this problem is reduced to showing that a certain set of
invariant polynomials forms an invariant basis. After establishing a certain
summation formula over Young diagrams, the latter problem is settled by
considering a recursion formula involving Bernoulli numbers.
  Keywords: polyhedral harmonics; cube; reflection groups; invariant theory;
invariant differential equations; generating functions; partitions; Young
diagrams; Bernoulli numbers.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: comp-gas