Table 1 List of notations.

set of nucleotides

ℕ

ℕ = {A, T, C, G}

reference sequence

W

w = "T AGT CGAGG"

read set

S

S = { "T AGT CG", "AGT CGA", "T CGAGG" }

k-mer

α or α^/

α = "T AG", α^/ = "CT A"

positive k-mer

_α +

α⁺ = "T AG"

negative k-mer

_α −

α⁻ = "CT A"

representative k-mer

_α +

α⁺ = "T AG"

k-molecule

$\hat{\alpha }={\alpha }^{+}=\left\{{\alpha }^{+},{\alpha }^{-}\right\}$

$\hat{\alpha }$ = {"T AG", "CT A"}

set of k-mers

ℤ(s, k)

ℤ("T AGT CG", 3) ={"TAG","AGT","GTC","TCG"}

set of k-molecules

S(s, k)

ℤ("T AGT C", 3) = {{"T AG", "CT A"}, {"AGT ", "ACT "}, {"GT C", "GAC"}, {"T CG", "CGA"}}