Kolakoski-$(3,1)$ Is a (Deformed) Model Set

[摘要] Unlike the (classical) Kolakoski sequence on the alphabet ${1,2}$, its analogueon ${1,3}$ can be related to a primitive substitution rule. Using this connection,we prove that the corresponding bi-infinite fixed point is a regular generic model setand thus has a pure point diffraction spectrum. The Kolakoski-$(3,1)$ sequence isthen obtained as a deformation, without losing the pure point diffraction property.

[学科分类] 数学（综合）

[关键词] Nevanlinna theory;meromorphic function;shared value