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- W2904312105 abstract "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 $X$." @default.
- W2904312105 created "2018-12-22" @default.
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- W2904312105 date "2018-12-19" @default.
- W2904312105 modified "2023-09-27" @default.
- W2904312105 title "Growth series of CAT(0) cubical complexes" @default.
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