Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Thue-Morse words and palindromic richness   We prove that the generalized Thue-Morse word $\mathbf{t}_{b,m}$ defined for
$b \geq 2$ and $m \geq 1$ as $\mathbf{t}_{b,m} = (s_b(n) \mod
m)_{n=0}^{+\infty}$, where $s_b(n)$ denotes the sum of digits in the base-$b$
representation of the integer $n$, has its language closed under all elements
of a group $D_m$ isomorphic to the dihedral group of order $2m$ consisting of
morphisms and antimorphisms. Considering simultaneously antimorphisms $\Theta
\in D_m$, we show that $\mathbf{t}_{b,m}$ is saturated by $\Theta$-palindromes
up to the highest possible level. Using the terminology generalizing the notion
of palindromic richness for more antimorphisms recently introduced by the
author and E. Pelantov\'a, we show that $\mathbf{t}_{b,m}$ is $D_m$-rich. We
also calculate the factor complexity of $\mathbf{t}_{b,m}$.

11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas