Morphic word

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