  Using the theory of PBW bases, one can realize the crystal $B(\infty)$ for
any semisimple Lie algebra over $\mathbf{C}$ using Kostant partitions as the
underlying set. In fact there are many such realizations, one for each reduced
expression for the longest element of the Weyl group. There is an algorithm to
calculate the actions of the crystal operators, but it can be quite
complicated. Here we show that, for certain reduced expressions, the crystal
operators can also be described by a much simpler bracketing rule. We give
conditions describing these reduced expressions, and show that there is at
least one example in every type except possibly $E_8$, $F_4$ and $G_2$. We then
discuss some examples.

Quantum Algebra;Combinatorics;Representation Theory