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a_1, ... a_P is ordered and indexed 0 to A-1.  Clearly when P = 1, the enumeration of the genotypes is trivially the same as the allele.
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Another important observation here is that for a genotype <math>(a_1, a_2, .. a_P)</math>, The <math>F(P, a_p)</math>th genotype to  <math>(a_1, a_2, .. a_P)</math> all end with <math>a_p</math>, this does not help distinguish the order, so we need to only examine the genotype <math>(a_1,..., a_{P-1})</math>.
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<math>a_1, ... a_P</math> is ordered and indexed 0 to A-1.  Clearly when P = 1, the enumeration of the genotypes is trivially the same as the allele.
    
when P > 1,  
 
when P > 1,  
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