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Growth series of some hyperbolic graphs and Salem numbers

Laurent Bartholdi·Tullio G. Ceccherini-Silberstein
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Abstract

Extending the analogous result of Cannon and Wagreich for the fundamental groups of surfaces, we show that, for the l-regular graphs X associated to regular tessellations of hyperbolic plane by m-gons, the denominators of the growth series (which are rational and were computed by Floyd and Plotnick) are reciprocal Salem polynomials. As a consequence, the growth rates of these graphs are Salem numbers. We then derive some regularity properties for the coefficients $a_n$ of the growth series: they satisfy $$Kλ^n-R 0$, $λ>1$.

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BibTeXRIS

Laurent Bartholdi, Tullio G. Ceccherini-Silberstein. 2000-12-14. Growth series of some hyperbolic graphs and Salem numbers. https://doi.org/10.1023/a%3A1014902918849

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