On generalized highly potential words (Q2215978)

The palindromic defect of a (finite) word is by definition the difference between the maximal possible number of distinct palindromic factors in this word (i.e., one more than the length of the word) and the effective number of distinct palindromic factors in the word. This definition can be extended to an infinite word as the (possibly infinite) supremum of the defects of all its factors. In the paper under review the authors generalize the notion of ``highly potential words'' introduced by the second author (see [Eur. J. Comb. 34, No. 6, 1028--1039 (2013; Zbl 1296.68112)]). Their recursive construction yields a family of infinite words, each of which having its set of factors closed under reversal. Further, these words are either periodic, or recurrent but not uniformly recurrent. The authors also obtain a characterization for the words in this family that have positive defect. Note that one can give, for Reference [11], a link to the slides of the cited talk: \url{https://www.fields.utoronto.ca/programs/scientific/12-13/words/slides/Bucci.pdf}.