Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arithmetic Self-Similarity of Infinite Sequences   We define the arithmetic self-similarity (AS) of a one-sided infinite
sequence sigma to be the set of arithmetic progressions through sigma which are
a vertical shift of sigma. We study the AS of several famlies of sequences,
viz. completely additive sequences, Toeplitz words and Keane's generalized
Morse sequences. We give a complete characterization of the AS of completely
additive sequences, and classify the set of single-gap Toeplitz patterns that
yield completely additive Toeplitz words. We show that every arithmetic
subsequence of a Toeplitz word generated by a one-gap pattern is again a
Toeplitz word. Finally, we establish that generalized Morse sequences are
specific sum-of-digits sequences, and show that their first difference is a
Toeplitz word.

30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph