  We revisit the problem of boundary excitations at a topological boundary or
junction defects between topological boundaries in non-chiral bosonic
topological orders in 2+1 dimensions. Based on physical considerations, we
derive a formula that relates the fusion rules of the boundary excitations, and
the "half-linking" number between condensed anyons and confined boundary
excitations. This formula is a direct analogue of the Verlinde formula. We also
demonstrate how these half-linking numbers can be computed in explicit Abelian
and non-Abelian examples. As a fundamental property of topological orders and
their allowed boundaries, this should also find applications in finding
suitable platforms realizing quantum computing devices.
