Combinatorial complexity of the signature of a natural tiling

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An additive model has been developed for calculating the combinatorial (Shannon-like) complexity of a signature of the natural tiling, which is used to describe the topological properties of micro- and mesoporous materials, in particular, zeolites. To calculate the complexity of this type, a Python program code has been compiled. The code was tested for tilings of a zeolite type. Correlations of the calculated complexity of a signature of the tiling and the combinatorial complexity of the tiling-generating structure were found.

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D. Banaru

Vernadsky Institute of Geochemistry and Analytical Chemistry of RAS

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Email: banaru@geokhi.ru
俄罗斯联邦, Moscow

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补充文件

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1. JATS XML
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2. Fig. 1. Tile [436] of the eponymous natural tiling of the pyrochlore structure Ca2Nb2O6F.

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3. Fig. 2. Scattering diagram of Htiling and IG (a), Htiling,tot and IG,tot (b) for zeolite-type frameworks.

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4. Fig. 3. The proportion of natural tiles of different complexity classes for zeolite-type frames.

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5. Supplementary materials
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