Some nonequiprobable models of random permutations

We consider a two-parameter model of random $n$-permutations, which is a generalisation of the classical model of $A$-permutations, and investigate the joint distribution of the number of $A$-cycles and $\bar A$-cycles under various realisations of the subset $A\subset X_n=\{1,2,\dots,n\}$.