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, 11:29, 31 January 2015
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| = Derivation for indexing the number of genotypes = | | = 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. |
| + | |
| + | a_1, ... a_p is ordered. Clearly when P = 1, the enumeration is of the genotypes is trivially the same as the allele. |
| + | |
| + | <math> |
| + | \begin{align} |
| + | G(a_1,.. , a_p) = \begin{cases} |
| + | a_1 &, p=1 \\ |
| + | F(a_p, p) + G(a_1,..,a_{p-1}) &, p \ne 1 |
| + | \end{cases} |
| + | \end{align} |
| + | </math> |