Flato-Fronsdal theorem for higher-order singletons

We prove a generalized Flato-Fronsdal theorem for higher-order, scalar and spinor, singletons. In the resulting infinite tower of bulk higher-spin fields, we point out the occurrence of partially-massless fields of all depths. This leads us to conjecture a holographic duality between a higher-spin gravity theory around AdS(d+1) with the afore- mentioned spectrum of fields, and a free CFTd of fundamental (higher-order) scalar and spinor singletons. As a first check of this conjecture, we find that the total Casimir energy vanishes at one loop.