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:⇒ A variant is normalized if and only if it is has no superfluous nucleotides on the left side and right parsimonious and left aligned. (definition of left parsimony) <br>
:⇒ A variant is normalized if and only if it is has no superfluous nucleotides on the left side and right parsimonious and left aligned. (definition of left parsimony) <br>
:⇒ A variant is normalized if and only if it is has no superfluous nucleotides on the left side and each allele does not end with the same type of nucleotide. (lemma 1) <br>
:⇒ A variant is normalized if and only if it is has no superfluous nucleotides on the left side and each allele does not end with the same type of nucleotide. (lemma 1) <br>
== Uniqueness ==
It is important that the normalization results in a unique representation of the variant. Before we begin the proof, intuitively, accept that any representation of a variant can be
transformed to another representation by removing or adding nucleotides from the reference sequence.
Now suppose there are 2 normalized variants A and B. Suppose A is at a different position from B and B is to the right of A (without loss in generality), this is not possible because by the definition of a normalized variant, it is left aligned,
and if they were at different positions, that means B may be left aligned to A since they represent the same variants leading to a contradiction. So A and B must be at the same position.
Now, suppose that A and B are of different lengths where B is longer than A, then this is not possible as B is then not parsimonious, so B can be trimmed to the same length as A.
Thus A and B have to be at the same position and have the same length and variant normalization is unique.
= Implementation =
= Implementation =
