Department of Discrete Mathematics

The Department of Discrete Mathematics was organized in 1994.

The staff of the Department inludes
A. M. Zubkov (Head of Department), B. A. Sevast'yanov, V. I. Afanas'ev, V. A. Vatutin, V. F. Kolchin, E. G. Krasulina, V. I. Kruglov, V. G. Mikhailov, V. E. Tarakanov, V. P. Chistyakov, and E. E. Dyakonova.

The specialized seminar is working in the Department.

The main directions of scientific activity of the Department of Discrete Mathematics include

• Discrete probability theory,
• Branching processes,
• Probabilistic methods in combinatorics.

Within the framework of these directions the following subjects are investigated: the stability criteria and the degeneracy criteria for critical branching processes with permutation of particles in the space; the functionals of particle paths in the case considered; the study of branching processes in random media; relations between random graphs and systems of random equations over finite fields; probability statistical inference on characteristics of discrete random sequences; inequalities for probability distributions; properties of convolutions of probability distributions on finite groups; algebraic properties of combinatorial structures.

New important results are obtained for evaluating different characteristics of critical branching processes. Effective methods are devising to study sums of related indicators. These methods are applied to investigate properties of processes of putting particles by cells, as well as to study random graphs and systems of random equations over finite fields. A series of problems of combinatorial graph theory are solved.