A class of enumerations of importance in genetics
Ronald Aylmer Fisher · Proceedings of the Royal Society B Biological Sciences · 1950
Abstract A number of enumerations arising in genetics, e. g. of sets of isomorphic genotypes, of modes of gamete formation, of the modes of formation of ordered and unordered tetrads, etc., have been found in previous work to yield solutions expressible as the mean powers of arbitrary degree of appropriate series of bases. These are such as to yield integral values of the mean for all integral exponents. The general combinatorial theorem governing this class of enumeration is given in § 2. Other Sections illustrate the method in operation by confirming and extending the genetic formulae so far established. In § 3·1 is a brief discussion of a partitional function which serves to enumerate the numbers of partitions of any partible number in a lattice of arbitrary dimensionality.