On the Expected Number of Distinct Gapped Palindromic Factors

An \(\alpha \)-gapped palindromic factor of a word is a factor of the form \(uv\overline{u}\), where \(\overline{u}\) is the reversal of u and where \(|uv|\le \alpha |u|\) for some fixed \(\alpha \ge 1\). We give an asymptotic estimate of the expected number of distinct palindromic factors in a random word for a memoryless source, where each letter is generated independently from the other, according to some fixed probability distribution on the alphabet.