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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.20598 |
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Table of Contents:
- In the field of compressed string indexes, recent work has introduced suffixient sets and their corresponding repetitiveness measure $χ$. In particular, researchers have explored its relationship to other repetitiveness measures, notably $r$, the number of runs in the Burrows--Wheeler Transform (BWT) of a string. Navarro et al. (2025) proved that $χ\leq 2r$, although empirical results by Cenzato et al. (2024) suggest that this bound is loose, with real data bounding $χ$ by around $1.13r$ to $1.33r$ when the size of the alphabet is $σ= 4$. To better understand this gap, we present two cases for the asymptotic tightness of the $χ\leq 2r$ bound: a general construction for arbitrary $σ$ values, and a binary alphabet case, consisting of de Bruijn sequences constructed by linear-feedback shift registers (LFSRs) from primitive polynomials over $\mathbb{F}_2$. The second is a novel characterization of which de Bruijn sequences achieve the literature run-minimal pattern for the cyclic BWT. Moreover, we show that de Bruijn sequences fail to close the gap for $σ\geq 3$.