  A broadcast network is a classical network with all source messages
collocated at a single source node. For broadcast networks, the standard
cut-set bounds, which are known to be loose in general, are closely related to
union as a specific set operation to combine the basic cuts of the network.
This paper provides a new set of network coding bounds for general broadcast
networks. These bounds combine the basic cuts of the network via a variety of
set operations (not just the union) and are established via only the
submodularity of Shannon entropy. The tightness of these bounds are
demonstrated via applications to combination networks.
