Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth infinite words over $n$-letter alphabets having same remainder
  when divided by $n$   Brlek et al. (2008) studied smooth infinite words and established some
results on letter frequency, recurrence, reversal and complementation for
2-letter alphabets having same parity. In this paper, we explore smooth
infinite words over $n$-letter alphabet $\{a_1,a_2,...,a_n\}$, where
$a_1<a_2<...<a_n$ are positive integers and have same remainder when divided by
$n$. And let $a_i=n\cdot q_i+r,\;q_i\in N$ for $i=1,2,...,n$, where
$r=0,1,2,...,n-1$. We use distinct methods to prove that (1) if $r=0$, the
letters frequency of two times differentiable well-proportioned infinite words
is $1/n$, which suggests that the letter frequency of the generalized Kolakoski
sequences is $1/2$ for 2-letter even alphabets; (2) the smooth infinite words
are recurrent; (3) if $r=0$ or $r>0 \text{ and }n$ is an even number, the
generalized Kolakoski words are uniformly recurrent for the alphabet $\Sigma_n$
with the cyclic order; (4) the factor set of three times differentiable
infinite words is not closed under any nonidentical permutation. Brlek et al.'s
results are only the special cases of our corresponding results.

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The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: econ