Special train algebras arising in genetics II

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Abstract
We shall extend some of the results of (7) to the case of multiple alleles, our primary concern being that of polyploidy combined with multiple alleles. Generalisations often tend to make the computations more involved as is expected. Fortunately here, the attempt to generalise has led to a new method which not only handles the case of multiple alleles, but is an improvement over the method used in (7) for the special case of polyploidy with two alleles. This method which consists essentially of expressing certain elements of the algebra in a so-called “ factored ” form, gives greater insight into the structure of a polyploidy algebra, and avoids a great deal of the computation with binomial coefficients, e.g. see (7), p. 46.

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