Pick a k-mer with minimal ratio \[ \frac{\text{charged occurrences}}{\text{total occurrences}} \] where ’total occurrences’ is the number of windows containing the k-mer, and ‘charged occurrences’ (my term) is the number of windows where the k-mer occurs as a prefix or suffix. Usually particular density is used for specific sequences, and density is the expected particular density on a random string. The cited Zheng, Kingsford, and Marçais (2021a 2.1.3) only states the fact for local schemes, but also makes it clear that the same positions are sampled, and thus that if the initial scheme is a minimizer scheme, the extended scheme is one as well.