Weak Abelian Periodicity of Infinite Words

作者：Avgustinovich Sergey; Puzynina Svetlana^*

来源：Theory of Computing Systems, 2016, 59(2): 161-179.

DOI：10.1007/s00224-015-9629-1

• Infinite word
• Abelian equivalence
• Periodicity
• Letter frequency
• Fixed points of morphisms
• Subshifts

An infinite word is called weak abelian periodic if it can be represented as an infinite concatenation of finite words with identical frequencies of letters. In the paper we undertake a general study of the weak abelian periodicity property. We consider its relation with the notions of balance and letter frequency, and study operations preserving weak abelian periodicity. We establish necessary and sufficient conditions for the weak abelian periodicity of fixed points of uniform binary morphisms. Finally, we discuss weak abelian periodicity in minimal subshifts.

• 出版日期2016-8