String Representation in Suffixient Set Size Space

Repetitiveness measures quantify how much repetitive structure a string contains and serve as parameters for compressed representations and indexing data structures. We study the measure $\chi$, defined as the size of the smallest suffixient set. Although $\chi$ has been studied extensively, its reachability, whether every string $w$ admits a string representation of size $O(\chi (w))$ words, has remained an important open problem. We answer this question affirmatively by presenting the first such representation scheme. Our construction is based on a new model, the substring equation system (SES), and we show that every string admits an SES of size $O(\chi (w))$.