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 Subgroups of direct products of groups invariant under the action of permutationson factorsD. A. Burov 3 Effective parallelization strategy for the solution of subset sum problems by the branch-and-bound methodR. M. Kolpakov, M. A. Posypkin 20 Collisions and incidence of vertices and components in the graph of $k$-fold iteration of the uniform random mappingV. O. Mironkin 38 Learning monotone functions with one error correctionS. N. Selezneva, Y. Liu 53 Local limit theorems for the generalized scheme of allocation of particles into ordered cellsA. N. Timashev 70 Maximal subclasses in classes of linear automata over finite fieldsA. A. Chasovskikh 88 Large Deviations for Branching Processes in Random Environment. IA. V. Shklyaev 102 The distribution of the maximal component volume for random $A$-mappingA. L. Yakymiv 116 Letter to the EditorsP. V. Roldugin 128