  Invertible fermionic topological (IFT) phases are gapped phases of matter
with nondegenerate ground states on any closed spatial manifold. When open
boundary conditions are imposed, nontrivial IFT phases support gapless boundary
degrees of freedom. Distinct IFT phases in one-dimensional space with an
internal symmetry group $G^{\,}_{f}$ have been characterized by a triplet of
indices $([(\nu,\rho)],[\mu])$. Our main result is an elementary derivation of
the fermionic stacking rules of one-dimensional IFT phases for any given
internal symmetry group $G^{\,}_{f}$ from the perspective of the boundary,
i.e., we give an explicit operational definition for the boundary
representation $([(\nu^{\,}_{\wedge},\rho^{\,}_{\wedge})],[\mu^{\,}_{\wedge}])$
obtained from stacking two IFT phases characterized by the triplets of boundary
indices $([(\nu^{\,}_{1},\rho^{\,}_{1})],[\mu^{\,}_{1}])$ and
$([(\nu^{\,}_{2},\rho^{\,}_{2})],[\mu^{\,}_{2}])$, respectively.
