  In this paper, we show generation and propagation of polynomial and
exponential moments, as well as global well-posedness of the homogeneous
binary-ternary Boltzmann equation. We also show that the co-existence of binary
and ternary collisions yields better generation properties and time decay, than
when only binary or ternary collisions are considered. To address these
questions, we develop for the first time angular averaging estimates for
ternary interactions. This is the first paper which discusses this type of
questions for the binary-ternary Boltzmann equation and opens the door for
studying moments properties of gases with higher collisional density.
