The model restricts itself to trees that can be obtained only by permuting child nodes of any of its non-terminal constituents, and it makes a simplifying assumption that the children of a node are permuted independently of any other node in the tree.
the overall probability simplifies to a product of constituent-level permutations: where n denotes a node, I(S) the set of all non-terminal (interior) nodes of the tree, d n are the children of the node n, and π is the permutation function.