Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graded algebras with prescribed Hilbert series   For any power series $a(t)$ with exponentially bounded nonnegative integer
coefficients we suggest a simple construction of a finitely generated monomial
associative algebra $R$ with Hilbert series $H(R,t)$ very close to $a(t)$. If
$a(t)$ is rational/algebraic/transcendental, then the same is $H(R,t)$. If the
growth of the coefficients of $a(t)$ is polynomial, in the same way we
construct a graded algebra $R$ preserving the polynomial growth of the
coefficients of its Hilbert series $H(R,t)$. Applying a classical result of
Fatou from 1906 we obtain that if a finitely generated graded algebra $R$ has a
finite Gelfand-Kirillov dimension, then its Hilbert series is either rational
or transcendental. In particular the same dichotomy holds for the Hilbert
series of finitely generated algebras $R$ with polynomial identity.

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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph