What is it about?

We prove the conjecture of Grosse-Kunstleve et al. that coordination sequences of periodic structures in n-dimensional Euclidean space are rational. This has been recently proven by Nakamura et al.; however, our proof is a straightforward application of classic techniques from automata theory.

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Why is it important?

We prove a conjecture appearing in Acta Crystallographica in 1996 using the techniques of automata theory.


Formal language theory, and specifically the theory of finite automata, provides a great framework to deal with periodic structures, especially its computational aspects. We hope this framework will find other uses in crystallography in the future.

Eryk Kopczynski
University of Warsaw

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This page is a summary of: Coordination sequences of periodic structures are rational via automata theory, Acta Crystallographica Section A Foundations and Advances, February 2022, International Union of Crystallography,
DOI: 10.1107/s2053273322000262.
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