Geodesic
Factor and arithmetic complexity of concatenating the $n!$
Čebyševskij sbornik, Tome 24 (2023) no. 4, pp. 341-344

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In this paper, we show that factor complexity of the infinite word $\mathfrak{F}_b$ 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, $\mathfrak{F}_b$ is a disjunctive word. In number theory, this kind of words is called rich numbers.
Keywords: factor complexity, equidistributed modulo $1$, Weyl's criterion, digital problems, factorials. 
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     author = {A. Duaa and M. Meisami},
     title = {Factor and arithmetic complexity of concatenating the $n!$},
     journal = {\v{C}eby\v{s}evskij sbornik},
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     publisher = {mathdoc},
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     number = {4},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2023_24_4_a20/}
}
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A. Duaa; M. Meisami. Factor and arithmetic complexity of concatenating the $n!$. Čebyševskij sbornik, Tome 24 (2023) no. 4, pp. 341-344. http://geodesic.mathdoc.fr/item/CHEB_2023_24_4_a20/