Abstract

We present a general theorem which can be used to identify the limiting distribution for a class of combinatorial schemata. For example, many parameters in random mappings can be covered in this way. Especially we can derive the limiting distibution of those points with a given number of total predecessors. 1 Introduction By a random mapping ' 2 Fn F = S n0 Fn we mean an arbitrary mapping ' : f1; : : : ; ng ! f1; : : : ; ng such that every mapping has equal probability n n . The main purpose of this paper is to obtain limit theorems, when n tends to innity, for special parameters in random mappings, e.g. for the number of image points. Since every random mapping ' 2 Fn has equal probability it suces to count the number of radom mappings ' 2 Fn satisfying a special property, e.g. that the number of image points equals k. By dividing this number by n n we get the probability of interest. In order to get the limit distribution for n !1 it is not necessary to know the exact v...

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