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On the rank of a class of bijective substitutions. (English) Zbl 0711.28007
It was conjectured by M. K. Mentzen that for any pair of rational numbers (k,n), where $$k\leq n$$, it is possible to construct an ergodic automorphism with rank n and spectral multiplicity k. The case (1,n) was solved by M. K. Mentzen [Bull. Pol. Acad. Sci., Math. 35, 417-424 (1987; Zbl 0675.28006)]. In this paper it is shown that a general class of bijective substitutions over r symbols has rank r and this theorem is used to solve Mentzens problem for the case (2,n).
Reviewer: R.Cowen

##### MSC:
 28D05 Measure-preserving transformations
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