Counting scattered palindromes in a finite word

08/05/2021

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by   Kalpana Mahalingam, et al.

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We investigate the scattered palindromic subwords in a finite word. We start by characterizing the words with the least number of scattered palindromic subwords. Then, we give an upper bound for the total number of palindromic subwords in a word of length n in terms of Fibonacci number F_n by proving that at most F_n new scattered palindromic subwords can be created on the concatenation of a letter to a word of length n-1. We propose a conjecture on the maximum number of scattered palindromic subwords in a word of length n with q distinct letters. We support the conjecture by showing its validity for words where q≥n/2.