Averaged coordination numbers of planar aperiodic tilings

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dc.creatorBaake, Michael
dc.creatorGrimm, Uwe
dc.date2005-09-18
dc.date.accessioned2026-07-07T06:25:07Z
dc.date.available2026-07-07T06:25:07Z
dc.descriptionWe consider averaged shelling and coordination numbers of aperiodic tilings. Shelling numbers count the vertices on radial shells around a vertex. Coordination numbers, in turn, count the vertices on coordination shells of a vertex, defined via the graph distance given by the tiling. For the Ammann-Beenker tiling, we find that coordination shells consist of complete shelling orbits, which enables us to calculate averaged coordination numbers for rather large distances explicitly. The relation to topological invariants of tilings is briefly discussed.
dc.description6 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0509038
dc.identifierhttp://arxiv.org/abs/math-ph/0509038
dc.identifierPhilosophical Magazine 86 (2006) 567-572
dc.identifierdoi:10.1080/14786430500269022
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96756
dc.subjectMathematical Physics
dc.subject52C23
dc.titleAveraged coordination numbers of planar aperiodic tilings
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