Coordination Sequences of Periodic Structures are Rational via Automata Theory

TL;DR

This paper proves that coordination sequences of periodic structures in Euclidean space are rational, using automata theory, providing a straightforward alternative to recent proofs.

Contribution

It offers a new proof of the rationality of coordination sequences based on automata theory, simplifying previous approaches.

Findings

Coordination sequences are rational functions.

Automata theory can be applied to periodic structures.

The proof is more straightforward than previous methods.

Abstract

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.