Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some relational structures with polynomial growth and their associated
  algebras I: Quasi-polynomiality of the profile   The profile of a relational structure $R$ is the function $\varphi_R$ which
counts for every integer $n$ the number $\varphi_R(n)$, possibly infinite, of
substructures of $R$ induced on the $n$-element subsets, isomorphic
substructures being identified. If $\varphi_R$ takes only finite values, this
is the Hilbert function of a graded algebra associated with $R$, the age
algebra introduced by P. J. Cameron.
  In this paper we give a closer look at this association, particularly when
the relational structure $R$ admits a finite monomorphic decomposition. This
setting still encompass well-studied graded commutative algebras like invariant
rings of finite permutation groups, or the rings of quasi-symmetric
polynomials. We prove that $\varphi_R$ is eventually a quasi-polynomial, this
supporting the conjecture that, under mild assumptions on $R$, $\varphi_R$ is
eventually a quasi-polynomial when it is bounded by some polynomial.

18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom