1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 l=11, k=5, w=l-k+1=7 lmer: *********** candidate minimizer kmers: ***** |***** ||***** |||***** ||||***** |||||***** ||||||***** ||||||| 8136192 // hashes in [0,9] | // rightmost minimal hash ***** // minimizer 1 2 3 4 5 6 7 8 l=11, k=5, w=7 ************ // n=12 text ***** ***** // first & last minimizer 81361921 // n-k+1 hashes of 5-mers -1--1-- // minimal hashes in first lmer ***** // minimizer is rightmost 1--1--1 // minimal hashes in second lmer ***** // reuse minimizer, instead of starting at rightmost 1. In the large-\(k\) limit, the minimizer schem - forward scheme - local scheme hierarchy collapses: minimizers already achieve the lower bound that holds for local schemes.