Arithmetical subword complexity of automatic sequences
We fully classify automatic sequences $a$ over a finite alphabet $\Omega$ with the property that each word over $\Omega$ appears is $a$ along an arithmetic progression. Using the terminology introduced by Avgustinovich, Fon-Der-Flaass and Frid, these are the automatic sequences with the maximal poss...
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| creator | Konieczny, Jakub Müllner, Clemens |
| description | We fully classify automatic sequences $a$ over a finite alphabet $\Omega$
with the property that each word over $\Omega$ appears is $a$ along an
arithmetic progression. Using the terminology introduced by Avgustinovich,
Fon-Der-Flaass and Frid, these are the automatic sequences with the maximal
possible arithmetical subword complexity. More generally, we obtain an
asymptotic formula for arithmetical (and even polynomial) subword complexity of
a given automatic sequence $a$. |
| doi_str_mv | 10.48550/arxiv.2309.03180 |
| format | Article |
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with the property that each word over $\Omega$ appears is $a$ along an
arithmetic progression. Using the terminology introduced by Avgustinovich,
Fon-Der-Flaass and Frid, these are the automatic sequences with the maximal
possible arithmetical subword complexity. More generally, we obtain an
asymptotic formula for arithmetical (and even polynomial) subword complexity of
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with the property that each word over $\Omega$ appears is $a$ along an
arithmetic progression. Using the terminology introduced by Avgustinovich,
Fon-Der-Flaass and Frid, these are the automatic sequences with the maximal
possible arithmetical subword complexity. More generally, we obtain an
asymptotic formula for arithmetical (and even polynomial) subword complexity of
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with the property that each word over $\Omega$ appears is $a$ along an
arithmetic progression. Using the terminology introduced by Avgustinovich,
Fon-Der-Flaass and Frid, these are the automatic sequences with the maximal
possible arithmetical subword complexity. More generally, we obtain an
asymptotic formula for arithmetical (and even polynomial) subword complexity of
a given automatic sequence $a$.</abstract><doi>10.48550/arxiv.2309.03180</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Formal Languages and Automata Theory Mathematics - Combinatorics Mathematics - Number Theory |
| title | Arithmetical subword complexity of automatic sequences |
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