Factor and arithmetic complexity of concatenating the 𝑛!
https://doi.org/10.22405/2226-8383-2023-24-4-341-344
Abstract
In this paper, we show that factor complexity of the infinite word F𝑏 is defined by concatenating base-𝑏 representations of the 𝑛! is full. Then we show that the arithmetic complexity of this word is full as well. On the other hand, F𝑏 is a disjunctive word. In number theory, this kind of words is called rich numbers.
About the Authors
Abdullah Duaa
Moscow Institute of Physics and Technology
Russian Federation
Russian Federation
Meisami Mahdi
University of Isfahan
Islamic Republic of Iran
Islamic Republic of Iran
References
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5. M. Rigo. 2014, “Formal languages, automata and numeration systems 1: Introduction to combinatorics on words”, John Wiley & Sons.
Review
For citations:
Duaa A., Mahdi M. Factor and arithmetic complexity of concatenating the 𝑛! Chebyshevskii Sbornik. 2023;24(4):341-344. (In Russ.) https://doi.org/10.22405/2226-8383-2023-24-4-341-344
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