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Lyndon words have been extensively studied in different contexts of free Lie algebra and combinatorics. All Lyndon and Nyldon words are primitive and any primitive class of words contains an unique Lyndon and an unique Nyldon word. This property motivated the study of Lyndon partial word which is primitive but all primitive classes of partial words may not contain a Lyndon partial word. In this paper we introduce two variants of Lyndon partial words namely Nyldon and inverse Lyndon partial words which are constructed from the decreasing alphabetical order. We compare the properties of the variants with those of Lyndon partial words. [ABSTRACT FROM AUTHOR]

We take into account the problem of identifying the repeated structure in a given pword v◊ of length l. We show that a pword v◊ is a cover of a pword u◊ if every letter of u◊ lies within an occurrence of v◊ in u◊ and v◊ is a border of u◊. Here, we examine string issues that are concerned with identifying recurring patterns in a given total word x. The total word's period p, a common regularity, captures x's repetition, since x is a prefix of a string created by concatenating p. We think about a challenge developed by expanding the scope of this repetitiveness idea by permitting overlaps between the segments that are repeated. We focus on a key issue in string processing: the compact representation of a word by its most frequent factors. The frequency cover, or the longest repeating factor, is a useful and simple form of quasi-periodicity in words that is proposed in this paper. [ABSTRACT FROM AUTHOR]

Many classes of finite words have noticeable properties with reference to their palindromic factors and one among them are the words having zero palindromic defect i.e., words rich in palindromes. In this paper we introduce rich partial word and discuss its combinatorial properties. We show that the palindromic richness of a partial word can be studied by including the positions of the missing symbols in that word. The significant difference between rich and rich partial word is that a rich word of length n contains exactly n + 1 distinct palindromic factors whereas a rich partial word of length n contains at least n + 1 distinct palindromic factors. These factors differ from the classical palindromes due to the presence of holes. [ABSTRACT FROM AUTHOR]