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Revision as of 12:18, 2 February 2015
, 12:18, 2 February 2015→Derivation for getting the index of a genotype in an enumerated list
\begin{align}
\begin{align}
G(a_1,.. , a_P) &= \| \{\text{genotypes of } a_P \text{ alleles for ploidy P}\} \| + G(a_1,.. , a_{P-1})\\
G(a_1,.. , a_P) &= \| \{\text{genotypes of } a_P \text{ alleles for ploidy P}\} \| + G(a_1,.. , a_{P-1})\\
&= F(P, a_P) + G(a_1,..,a_{P-1})
&= F(P, a_P) + G(a_1,..,a_{P-1}) \\
&= F(P, a_P) + F(P-1, a_{P-1}) + G(a_1,..,a_{P-2}) \\
&= F(P, a_P) + F(P-1, a_{P-1}) + ... + F(1,,a_1) \\
&= \sum_{k=1}^P F(k, a_k) \\
\end{align}
\end{align}
</math>
</math>
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