TY - JOUR

T1 - Weak Abelian Periodicity of Infinite Words

AU - Avgustinovich, Sergey

AU - Puzynina, Svetlana

PY - 2016/8/1

Y1 - 2016/8/1

N2 - 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.

AB - 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.

KW - Abelian equivalence

KW - Fixed points of morphisms

KW - Infinite word

KW - Letter frequency

KW - Periodicity

KW - Subshifts

UR - http://www.scopus.com/inward/record.url?scp=84927546446&partnerID=8YFLogxK

U2 - 10.1007/s00224-015-9629-1

DO - 10.1007/s00224-015-9629-1

M3 - Article

AN - SCOPUS:84927546446

VL - 59

SP - 161

EP - 179

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 2

ER -