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| Reference : On the Recognizability of Self-Generating Sets |
| Scientific journals : Article | |||
| Engineering, computing & technology : Computer science Physical, chemical, mathematical & earth Sciences : Mathematics | |||
| http://hdl.handle.net/2268/12140 | |||
| On the Recognizability of Self-Generating Sets | |
| English | |
| Kärki, Tomi [ > > ] | |
Lacroix, Anne  [Université de Liège - ULg > Département de mathématique > Mathématiques discrètes >] | |
| Rigo, Michel [Université de Liège - ULg > Département de mathématique > Mathématiques discrètes >] | |
| 2010 | |
| Journal of Integer Sequences | |
| 13 | |
| Article 10.2.2 | |
| International | |
| [en] numeration system ; self-generating set ; Cobham's theorem ; automatic sequences ; syndeticity | |
| [en] Let I be a finite set of integers and F be a finite set of maps of the form n->k_i n + l_i with integer coefficients. For an integer base k>=2, we study the k-recognizability of the minimal set X of integers containing I and satisfying f(X)\subseteq X for all f in F. In particular, solving a conjecture of Allouche, Shallit and Skordev, we show under some technical conditions that if two of the constants k_i are multiplicatively independent, then X is not k-recognizable for any k>=2. | |
| Researchers | |
| http://hdl.handle.net/2268/12140 | |
| http://www.cs.uwaterloo.ca/journals/JIS/VOL13/Rigo/rigo6.html | |
| Concerned with sequences A000045, A000201, A001950, A003754, A003849, A052499. |
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