On maximal repetitions of arbitrary exponent

TL;DR

This paper extends the study of maximal repetitions in words by analyzing those with exponents strictly greater than 1, building on prior work that focused on exponents at least 2.

Contribution

It generalizes the linear bound on the sum of exponents of maximal repetitions to include all exponents greater than 1.

Findings

Sum of exponents of maximal repetitions > 1 is linear in word length

Extends previous results from exponent ≥ 2 to all > 1

Provides new insights into the structure of repetitions in words

Abstract

The first two authors have shown [KK99,KK00] that the sum the exponent (and thus the number) of maximal repetitions of exponent at least 2 (also called runs) is linear in the length of the word. The exponent 2 in the definition of a run may seem arbitrary. In this paper, we consider maximal repetitions of exponent strictly greater than 1.