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Values for this bound can be obtained from standard tables for the Poisson distribution, but the following representative cases will give some feeling for the numbers involved. Setting k = 2 and l = 32 (so that  contains 232@ 4.3 X 109 distinct elements) we get: |
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Even for the small values of N considered here it is clear that a great many schemata will receive a significant number of trials. Moreover the figures given are quite conservative since at least one schema defined on each distinct set of positions must receive at least 1 trial in kh,whereas the bound assumes none receive more than 1 in  . |
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The figures just given also hint at a compact way for storing a great deal of information about schemata. Suppose that the object is to store the relative rank of a large number of schemata where, say, x ranks higher than x' when µx > µx'. Let us limit the number of ranks to M (e.g., by dividing the range of µ into M intervals and assigning x the same rank as x' if their average payoffs, µx and µx', fall in the same interval). Now with a set of M elements,  , it is possible to represent the rank of a given schema x by the number of instances of x, Aj Îx, in the set. That is, if x has rank m < M, there will be m instances of x in  ,  . Note that there is no requirement that Aj = Aj' for j ¹ j', so that given some other schema x' we may have AjÎx' but Aj' Ï x'. Thus the same instances used to represent the rank of x can be used in differing numbers to represent the ranks of other schemata. |
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For example, given the 8 individuals |
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