On estimation of the probability of absence of collisions of some random mappings

Let X and Y be finite sets and φ: (X,Y) →Y be a mapping. Consider a random mapping i → φ(x_i,y_i), where x_i are arbitrarily chosen from the set X, whereas (y_i) is a random sample from Y without replacement. A two-sided bound is derived for the probability of absence of collisions of this mapping. A case of mapping, defined as φ(x, y)=x+ y modulo n, is considered in particular. The results may be used in the selection of identification codes. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 132–137, January–February, 2000.