## Morphisms preserving the set of words coding three interval exchange.(English)Zbl 1247.68207

Summary: Any amicable pair $$\varphi , \psi$$ of Sturmian morphisms enables a construction of a ternary morphism $$\eta$$ which preserves the set of infinite words coding 3-interval exchange. We determine the number of amicable pairs with the same incidence matrix in SL$$^{\pm }(2,\mathbb N)$$ and we study incidence matrices associated with the corresponding ternary morphisms $$\eta$$.

### MSC:

 68R15 Combinatorics on words 08A50 Word problems (aspects of algebraic structures)
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### References:

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