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PERIODIC UNIQUE BETA-EXPANSIONS: THE SHARKOVSKII ORDERING
 

Summary: PERIODIC UNIQUE BETA-EXPANSIONS:
THE SHARKOVSKII ORDERING
JEAN-PAUL ALLOUCHE, MATTHEW CLARKE, AND NIKITA SIDOROV
To O. M. Sharkovskii on the occasion of his 70th birthday
ABSTRACT. Let (1, 2). Each x [0, 1
-1 ] can be represented in the form
x =

k=1
k-k
,
where k {0, 1} for all k (a -expansion of x). If > 1+

5
2 , then, as is well known, there
always exist x (0, 1
-1 ) which have a unique -expansion.
In the present paper we study (purely) periodic unique -expansions and show that for each
n 2 there exists n [1+

  

Source: Allouche, Jean-Paul - Laboratoire de Recherche en Informatique, Université de Paris-Sud 11

 

Collections: Computer Technologies and Information Sciences