New variants of many-particle Faddeev equations

New generalizations of the Faddeev equations to arbitrary systems of particles are given. Unlike the known equations, the present ones are formulated in terms of the quantities corresponding to systems of particles with smaller number of pair interactions compared to the initial system (by one, two, etc.) and only in particular cases this is the same as the reduction to subsystems with a smaller number of particles. The method of constructing the equations with connected kernels for $T$-, $G$-operators and wave functions of $N$-particle systems with an arbitrary number $m$ ($m\leqslant N(N?1)/2$) of pair potentials is described. Equations for the four-particle $T$-operator are considered in detail.