Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limit elements in the configuration algebra for a cancellative monoid   We introduce two spaces $\Omega(\Gamma,G)$ and $\Omega(P_{\Gamma,G})$ of
pre-partition functions and of opposite series, respectively, which are
associated with a Cayley graph $(\Gamma,G)$ of a cancellative monoid $\Gamma$
with a finite generating system $G$ and with its growth function
$P_{\Gamma,G}(t)$. Under mild assumptions on $(\Gamma,G)$, we introduce a
fibration $\pi_\Omega:\Omega(\Gamma,G)\to \Omega(P_{\Gamma,G})$ equivariant
with a $\Z_{\ge0}$-action, which is transitive if it is of finite order. Then,
the sum of pre-partition functions in a fiber is a linear combination of
residues of the proportion of two growth functions $P_{\Gamma,G}(t)$ and
$P_{\Gamma,G}\mathcal{M}(t)$ attached to $(\Gamma,G)$ at the places of poles on
the circle of the convergent radius.

25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
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The categories of this paper are: q-fin