Relational Fine and Wilf words

The theorem of Fine and Wilf for relational periods

We consider relational periods, where the relation is a compatibility relation on words induced by a relation on letters. We prove a variant of the theorem of Fine and Wilf for a (pure) period and a relational period.

Interaction Properties of Relational Periods

Similarity relations, i.e., compatibility relations on words induced by relations on letters were introduced as a generalization of partial words in [9](i). There and in [10, 11] the main focus was on the effect of these relations on coding properties and on the defect theorem of words. In the article [8] we started the study of the interaction properties of periods with respect to similarity r...

Fine and Wilf Words for Any Periods

Partial words and a theorem of Fine and Wilf revisited

A word of length n over a 1nite alphabet A is a map from {0; : : : ; n − 1} into A. A partial word of length n over A is a partial map from {0; : : : ; n− 1} into A. In the latter case, elements of {0; : : : ; n−1} without image are called holes (a word is just a partial word without holes). In this paper, we extend a fundamental periodicity result on words due to Fine and Wilf to partial words...

Abelian periods, partial words, and an extension of a theorem of Fine and Wilf

Recently, Constantinescu and Ilie proved a variant of the wellknown periodicity theorem of Fine and Wilf in the case of two relatively prime abelian periods and conjectured a result for the case of two nonrelatively prime abelian periods. In this paper, we answer some open problems they suggested. We show that their conjecture is false but we give bounds, that depend on the two abelian periods,...