## Rocky Mountain Journal of Mathematics

### A short proof of a theorem of Cobham on substitutions

#### Abstract

This paper is concerned with the lengths of constant length substitutions that generate topologically conjugate systems. We show that if the systems are infinite, then these lengths must be powers of the same integer. This result is a dynamical formulation of a special case of a 1969 theoretical computer science result of Cobham [{\bf1}]. Our proof is rather simple.

#### Article information

Source
Rocky Mountain J. Math., Volume 44, Number 1 (2014), 19-22.

Dates
First available in Project Euclid: 2 June 2014

https://projecteuclid.org/euclid.rmjm/1401740488

Digital Object Identifier
doi:10.1216/RMJ-2014-44-1-19

Mathematical Reviews number (MathSciNet)
MR3216006

Zentralblatt MATH identifier
1298.37007

#### Citation

Coven, Ethan M.; Dykstra, Andrew; Lemasurier, Michelle. A short proof of a theorem of Cobham on substitutions. Rocky Mountain J. Math. 44 (2014), no. 1, 19--22. doi:10.1216/RMJ-2014-44-1-19. https://projecteuclid.org/euclid.rmjm/1401740488

#### References

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• E.M. Coven, M. Keane and M. LeMasurier, A characterization of the Morse minimal set up to topological conjugacy, Ergod. Theor. Dynam. Syst. 28 (2008), 1443-1451.
• F.M. Dekking, The spectrum of dynamical systems arising from substitutions of constant length, Z. Wahrschein. Verw. Geb. 41 (1977/78), 221-239.
• F. Durand, Cobham-Semenov theorem and $\n^d$-subshifts, Theor. Comp. Sci. 391 (2008), 20-38.
• S. Eilenberg, Automata, languages, and machines, Pure Appl. Math. 58, Academic Press, New York, 1974. \noindentstyle