Styopochkina M. (Min, max)-equivalence of finite posets and positive definiteness of the quadratic Tits form

The disertation is devoted to the study of the quadratic Tits form of finite posets by the method of (min, max)-equivalence, and applications of received results in the theory of representations of posets. The main results of the disertation are classifications the posets with positive Tits form and P-critical posets. It is proved that any poset with positive Tits form of order n>7 is serial, and that a poset is P-critical if and only if it is (min, max)-equivalent to some critical Kleiner set. In the last chapter of the dissertation the indicated results apply to the study of posets with the category of injective representations to be of $rep$-finite type.