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Single Nucleotide Polymorphism (SNP)

A variation in a DNA sequence at a single nucleotide position between individuals or populations, often associated with genetic differences.
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The statement of the theorem

Let SrefS_{ref} be the reference sequence and SsampleS_{sample} be the sample sequence, both aligned to a common coordinate system. Consider a locus ii at position pp. A Single Nucleotide Polymorphism (SNP) exists at (p,i)(p, i) if the nucleotide base Bsample(p)B_{sample}(p) differs from the reference base Bref(p)B_{ref}(p): SNP(p,i)  ⟺  Bsample(p)≠Bref(p)SNP(p, i) \iff B_{sample}(p) \neq B_{ref}(p) \nThis difference is quantified by the Hamming distance dH(Sref,Ssample)d_H(S_{ref}, S_{sample}) over the entire genome, where dH(Sref,Ssample)=∑p=1LI(Bref(p)≠Bsample(p))d_H(S_{ref}, S_{sample}) = \sum_{p=1}^{L} \mathbb{I}(B_{ref}(p) \neq B_{sample}(p)), and I(⋅)\mathbb{I}(\cdot) is the indicator function.