Auto-similarity in Rational Base Number Systems View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2013

AUTHORS

Shigeki Akiyama , Victor Marsault , Jacques Sakarovitch

ABSTRACT

This work is a contribution to the study of set of the representations of integers in a rational base number system. This prefix-closed subset of the free monoid is naturally represented as a highly non regular tree whose nodes are the integers and whose subtrees are all distinct. With every node of that tree is then associated a minimal infinite word (and a maximal infinite word).The main result is that a sequential transducer which computes for all n the minimal word associated with n + 1 from the one associated with n, has essentially the same underlying graph as the tree itself.These infinite words are then interpreted as representations of real numbers; the difference between the numbers represented by the maximal and minimal word associated with n is called the span of n. The preceding construction allows to characterise the topological closure of the set of spans. More... »

PAGES

34-45

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-40579-2_7

DOI

http://dx.doi.org/10.1007/978-3-642-40579-2_7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1025503938


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