A random mapping (T, Pj) of a finite set V into itself is studied. We give a new proof of the
fundamental lemma of [6]. Our method leads to the derivation of several results which cannot …

ON A SIMPLE FORMULA FOR RANDOM MAPPINGS AND ITS APPLICATIONS 1. Let N be the
set of natural numbers. Assume that two sequences E Page 1 J. Appl. Prob. 17,403-414 (1980) …

A random bipartite mapping (T; P j, Q j) of a finite set V= V 1∪ V 2 into itself is considered.
Wc determine the exact distributions of several numerical characteristics (for example the …

Let X{x, x,..., x,} be a finite set and let T be a single-valued mapping of X into itself.
Themapping T can be represented as an oriented graph G whose vertices are the elements …

In § 2 we tabulate for easy reference probability distributions associated with some functions
of random mappings on large sets (eg, number of points on cycles, size of the component …

p,4nPl=z Page 1 A RANDOM MAPPING 829 LIMIT THEOREMS FOR A CHARACTERISTIC
OF A RANDOM MAPPING YU. L. PAVLOV (Translated by K. Duff) 1. In Stepanov’s paper [1] …

1. Let, denote the family of all mappings of the finite set 9.1 of n elements into itself with the
underlying condition that the mapping height does not exceed h, ie, the height of trees of the …

A Random Mapping Space (X, J, P) is a triplet, where X is a finite set of elements x of
cardinality n, J is a set of transformations T of X into X, and P is a probability measure over J …

Let T be a single-valued mapping of the finite set X{x, x2, Xm} into itself and Gr the graph of
the mapping whose vertices are elements of the set X,,, two vertices xi, xj being joined in Gr …

Let ℱn be the set of random mappings ϕ:{1,…, n}→{1,…, n}(such that every mapping is
equally likely). For x ε {l,…, n} the elements are called the predecessors of x. Let Nr denote …