Abstract

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. A word equal to its reversal is a palindrome. Partial words and palindromes play a vital role in molecular biology and language theory which inspired and initiated a unified study of rich words and partial words. 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.

Keywords and Phrases

Palindromes, rich words, factors, partial words, primitivity.

A.M.S. subject classification

68Q45, 68R15.

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