The number of disordered covers of a finite set by subsets having fixed cardinalities

This article describes a new type of combinatorial numbers which calculate amount of the covers of a finite set by subsets having fixed cardinalities – parameters of numbers. A series of relations and identities are proved for them. Some sums of these numbers are computed. Special cases of new combinatorial numbers with parameters satisfying certain relations are investigated. Several other applications of these numbers in discrete mathematics are shown.