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Revision as of 11:34, 31 January 2015
, 11:34, 31 January 2015→Derivation for indexing the number of genotypes
An important observation here is that the enumeration of a A alleles for a given P ploidy, the enumeration of A-1 alleles for P ploidy is a subsequence.
An important observation here is that the enumeration of a A alleles for a given P ploidy, the enumeration of A-1 alleles for P ploidy is a subsequence.
a_1, ... a_p is ordered. Clearly when P = 1, the enumeration is of the genotypes is trivially the same as the allele.
a_1, ... a_P is ordered and indexed 0 to A-1. Clearly when P = 1, the enumeration is of the genotypes is trivially the same as the allele.
when P > 1,
<math>
<math>
\begin{align}
\begin{align}
G(a_1,.. , a_p) = \begin{cases}
G(a_1,.. , a_P) &= \| \{ \text{genotypes of a_P alleles for ploidy P} \} \| \\
&= F(a_P, P) + G(a_1,..,a_{P-1})
F(a_p, p) + G(a_1,..,a_{p-1}) &, p \ne 1
\end{align}
\end{align}
</math>
</math>
= Algorithm for enumerating the genotypes given A ploidy and alleles =
= Algorithm for enumerating the genotypes given A ploidy and alleles =
