Department of Mathematics FNSPE, Czech Technical University in
13, 120 00
Accepted: 3 February 2012
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 SL±(2,ℕ) and we study incidence matrices associated with the corresponding ternary morphisms η.
Mathematics Subject Classification: 68R15
Key words: Interval exchange / three interval exchange / amicable Sturmian morphisms / incidence matrix of morphism
We acknowledge financial support by the Czech Science Foundation grant 201/09/0584 and by the grants MSM6840770039 and LC06002 of the Ministry of Education, Youth, and Sports of the Czech Republic. We also thank the CTU student grant SGS10/085/OHK4/1T/14 and SGS11/162/OHK4/3T/14.
© EDP Sciences 2012