The widespread use of \(k\) -mers in bioinformatics has enabled efficient genomic sequence analysis across various tasks. However, the impact of \(k\) -mer size remains unclear, as complex bioinformatics pipelines obscure its influence with noise. The choice of \(k\) is often arbitrary and rarely justified in literature or tutorials. Moreover, methods using multiple \(k\) -mer sizes face substantial computational challenges. Most methods rely on well-defined \(k\) -mer objects like de Bruijn graphs, Jaccard similarity, Bray-Curtis dissimilarity, and \(k\) -mer spectra. The role of \(k\) -mer size in these objects is intuitive and described by various metrics. Exploring these objects across \(k\) -mer sizes enables robust analyses and new applications. However, how \(k\) -mer objects evolve with size remains elusive, and modern substring indices struggle to explore them across sizes. We introduce the \(Pro\) k \(rustean \) graph, a novel substring index that tracks \(k\) -mer set transformations across sizes. Built on this index, our framework efficiently computes \(k\) -mer-based quantities for all sizes, with complexity independent of the range and dependent only on maximal repeats. For example, counting maximal simple paths in de Bruijn graphs for \(k = 1, \dots , 100\) takes seconds on a gigabase-scale dataset. We demonstrate this with experiments in pangenomics and metagenomics. The \(Pro\) k \(rustean \) graph is space-efficiently constructed from the Burrows-Wheeler Transform. Our implementation is available at: https://github.com/KoslickiLab/prokrustean . The full version of this manuscript, including construction and four application algorithms, is available at: https://doi.org/10.1101/2023.11.21.568151 .