Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth series of CAT(0) cubical complexes   Let $X$ be a CAT(0) cubical complex. The growth series of $X$ at $x$ is
$G_{x}(t)=\sum_{y \in Vert(X)} t^{d(x,y)}$, where $d(x,y)$ denotes
$\ell_{1}$-distance between $x$ and $y$. If $X$ is cocompact, then $G_{x}$ is a
rational function of $t$. In the case when $X$ is the Davis complex of a
right-angled Coxeter group it is a well-known that
$G_{x}(t)=1/f_{L}(-t/(1+t))$, where $f_{L}$ denotes the $f$-polynomial of the
link $L$ of a vertex of $X$. We obtain a similar formula for general cocompact
$X$. We also obtain a simple relation between the growth series of individual
orbits and the $f$-polynomials of various links. In particular, we get a simple
proof of reciprocity of these series ($G_{x}(t)=\pm G_{x}(t^{-1})$) for an
Eulerian manifold $X$.

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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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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: q-fin
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th