Abstract
We study the probability that the edges of a random cycle of k vertices in the lattice \({\{1,\ldots,n\}^s}\) do not contain more lattice points than the k vertices of the cycle. Then we introduce the chromatic zeta function of a graph to generalize this problem to other configurations induced by a given graph \({\mathcal H}\).
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The author passed away on May 15, 2016. The final editing of this paper was carried out by Pablo Fernández Gallardo and Gyula Károlyi.
The research was supported by MINECO project MTM2014-56350-P and ICMAT Severo Ochoa project SEV-2011-0087.
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Cilleruelo, J. Visible lattice points and the chromatic zeta function of a graph. Acta Math. Hungar. 151, 1–7 (2017). https://doi.org/10.1007/s10474-016-0678-y
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DOI: https://doi.org/10.1007/s10474-016-0678-y