Any amicable pair , of Sturmian morphisms enables a construction of a ternary morphism 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 .
Any amicable pair , of Sturmian morphisms enables a construction of a ternary morphism 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 .
We consider positional numeration systems with negative real base , where , and study the extremal representations in these systems, called here the greedy and lazy representations. We give algorithms for determination of minimal and maximal -representation with respect to the alternate order. We also show that both extremal representations can be obtained as representations in the positive base with a non-integer alphabet. This enables us to characterize digit sequences admissible as greedy...
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