  We consider charmless weak decays of beauty-baryons into decuplet baryons and
pseudoscalar mesons in a general framework based on $SU(3)$-flavor
decomposition of the decay amplitudes. The dynamical assumption independent
$SU(3)$ analysis accounts for the effects of an arbitrarily broken $SU(3)$
symmetry in these decays. An alternative approach in terms of quark diagrams is
also provided and compared with the $SU(3)$ decomposition in the limit of exact
$SU(3)$-flavor symmetry. Furthermore, the symmetries of the effective
Hamiltonian is used to relate or neglect reduced $SU(3)$ amplitudes to derive
several sum rule relations between amplitudes and relations between $CP$
asymmetries in these decays and identify those that hold even if $SU(3)$ is
broken.
