Morphisms preserving the set of words coding three interval exchange

Abstract

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

16 pages