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

TL;DR

This paper establishes tighter upper bounds on the number of maximal -gapped repeats and palindromes in words of length n, improving understanding of their combinatorial complexity.

Contribution

It provides new, sharper upper bounds on the counts of maximal -gapped repeats and palindromes, advancing theoretical knowledge in string combinatorics.

Findings

Upper bound for maximal -gapped repeats: approximately 3(^2/6 + 5/2)  n

Upper bound for maximal -gapped palindromes: approximately 7 (^2 / 6 + 1/2)  n

Results improve previous bounds on the combinatorial complexity of these structures.

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 $7 (\pi^2 / 6 + 1/2) \alpha n - 5 n - 1$, respectively.