On the enumerating series of an abstract numeration system

Details On the enumerating series of an abstract numeration system On the enumerating series of an abstract numeration system

2011-08-29

arxiv.org/abs/1108.5711v1

Computer Science

Discrete Mathematics

presented at the Journ\'ees Montoises d'Informatique Th\'eorique 2010, Sept. 2010, Amiens (France)

Scientific paper

It is known that any rational abstract numeration system is faithfully, and effectively, represented by an N-rational series. A simple proof of this result is given which yields a representation of this series which in turn allows a simple computation of the value of words in this system and easy constructions for the recognition of recognisable sets of numbers. It is also shown that conversely it is decidable whether an N-rational series corresponds to a rational abstract numeration system.

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