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Difference between revisions of "Morphic word"

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(Start article: Morphic word)
 
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====References====
 
====References====
* Allouche, Jean-Paul; Shallit, Jeffrey ''Automatic Sequences: Theory, Applications, Generalizations'' Cambridge University Press (2003) ISBN 978-0-521-82332-6 {{ZBL|1086.11015}}
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* Allouche, Jean-Paul; Shallit, Jeffrey ''Automatic Sequences: Theory, Applications, Generalizations'' Cambridge University Press (2003) {{ISBN|978-0-521-82332-6}} {{ZBL|1086.11015}}
* Lothaire, M. ''Combinatorics on Words'' (2nd ed.) Encyclopedia of Mathematics and Its Applications '''17''''  Cambridge University Press (1997) ISBN 0-521-59924-5 {{ZBL|0874.20040}}
+
* Lothaire, M. ''Combinatorics on Words'' (2nd ed.) Encyclopedia of Mathematics and Its Applications '''17''''  Cambridge University Press (1997) {{ISBN|0-521-59924-5}} {{ZBL|0874.20040}}
* Lothaire, M. ''Algebraic Combinatorics on Words'' Encyclopedia of Mathematics and Its Applications '''90''' Cambridge University Press (2011 [2002]) ISBN 978-0-521-18071-9 {{ZBL|1221.68183}}
+
* Lothaire, M. ''Algebraic Combinatorics on Words'' Encyclopedia of Mathematics and Its Applications '''90''' Cambridge University Press (2011 [2002]) {{ISBN|978-0-521-18071-9}} {{ZBL|1221.68183}}
* Pytheas Fogg, N. (ed.) ''Substitutions in dynamics, arithmetics and combinatorics'' Lecture Notes in Mathematics '''1794''' Springer (2002) ISBN 978-3-540-44141-0 {{ZBL|1014.11015}}
+
* Pytheas Fogg, N. (ed.) ''Substitutions in dynamics, arithmetics and combinatorics'' Lecture Notes in Mathematics '''1794''' Springer (2002) {{ISBN|978-3-540-44141-0}} {{ZBL|1014.11015}}
  
 
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Latest revision as of 09:30, 12 October 2023

A infinite word over an alphabet $A$ which is invariant under a non-erasing endomorphism $\phi$ of the free monoid $A^*$: that is, a map $\phi : A \rightarrow A^*$ which does not map any letter of $A$ to the empty word.

Examples: the Thue–Morse sequence on $A = \{a,b\}$ is invariant under $a \mapsto ab$, $b \mapsto ba$; the Fibonacci word on $A = \{a,b\}$ is invariant under $a \mapsto ab$, $b \mapsto a$.

See also: D0L-sequence.

References

  • Allouche, Jean-Paul; Shallit, Jeffrey Automatic Sequences: Theory, Applications, Generalizations Cambridge University Press (2003) ISBN 978-0-521-82332-6 Zbl 1086.11015
  • Lothaire, M. Combinatorics on Words (2nd ed.) Encyclopedia of Mathematics and Its Applications 17' Cambridge University Press (1997) ISBN 0-521-59924-5 Zbl 0874.20040
  • Lothaire, M. Algebraic Combinatorics on Words Encyclopedia of Mathematics and Its Applications 90 Cambridge University Press (2011 [2002]) ISBN 978-0-521-18071-9 Zbl 1221.68183
  • Pytheas Fogg, N. (ed.) Substitutions in dynamics, arithmetics and combinatorics Lecture Notes in Mathematics 1794 Springer (2002) ISBN 978-3-540-44141-0 Zbl 1014.11015
How to Cite This Entry:
Morphic word. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Morphic_word&oldid=37190