Robert Mercas

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The paper approaches the classical combinatorial problem of freeness of words, in the more general case of partial words. First, we propose an algorithm that tests efficiently whether a partial word is kfree or not. Then, we show that there exist arbitrarily many cube-free infinite partial words containing an infinite number of holes, over binary alphabets;(More)
A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of length n is bounded by 2n since at each position there are at most two distinct squares whose last occurrence start. In this paper, we investigate the problem of counting distinct squares in partial words, or sequences over a finite alphabet that may have(More)
The concept of runs, i.e. maximal periodicity or maximal occurrence of repetitions, coined by Iliopoulos et al. [10] when analysing Fibanacci words, has been introduced to represent in a succinct manner all occurrences of repetitions in a word. It is known that there are only O(n) many of them in a word of length n from Kolpakov and Kucherov [11] who proved(More)
Pseudo-repetitions are a natural generalization of the classical notion of repetitions in sequences. We solve fundamental algorithmic questions on pseudo-repetitions by application of insightful combinatorial results on words. More precisely, we efficiently decide whether a word is a pseudorepetition and find all the pseudo-repetitive factors of a word.(More)
A well known result of Fraenkel and Simpson states that the number of distinct squares in a full word of length n is bounded by 2n since at each position there are at most two distinct squares whose last occurrence start. In this paper, we investigate squares in partial words with one hole, or sequences over a finite alphabet that have a “do not know”(More)
We initiate a study of languages of partial words related to regular languages of full words. First, we investigate the possibility of expressing a regular language of full words as the image of a partial-words-language through a substitution that only replaces the hole symbols of the partial words by a finite set of letters. Results regarding the(More)
This paper approaches the combinatorial problem of Thue freeness for partial words. Partial words are sequences over a finite alphabet that may contain a number of “holes.” First, we give an infinite word over a three-letter alphabet which avoids squares of length greater than two even after we replace an infinite number of positions with holes. Then, we(More)
Erdös raised the question whether there exist infinite abelian square-free words over a given alphabet (words in which no two adjacent subwords are permutations of each other). Infinite abelian square-free words have been constructed over alphabets of sizes as small as four. In this paper, we investigate the problem of avoiding abelian squares in partial(More)