Improved Upper Bounds on all Maximal $\alpha$-gapped Repeats and Palindromes

Abstract

We show that the number of all maximal $\alpha$-gapped repeats and palindromes of a word of length $n$ is at most $3({\pi }^2/6+5/2)\alpha n$ and $7({\pi }^2/6+1/2)\alpha n-5n-1$, respectively.