Cycle structure of random permutations on the set of two-color elements. I

Random equiprobable permutations on the set of elements marked by two colors are considered. The cardinality of the set of elements of one color is an arbitrary function of the permutation order. This first part of the paper contains statements on the characteristics of one-color cycles. Results may be used in the study of the cycle structure of polynomial transforms acting on finite rings of some types.