  The generalization of $A_r$ statistics, including bosonic and fermionic
sectors, is performed by means of the so-called Jacobson generators. The
corresponding Fock spaces are constructed. The Bargmann representations are
also considered. For the bosonic $A_r$ statistics, two inequivalent Bargmann
realizations are developed. The first (resp. second) realization induces, in a
natural way, coherent states recognized as Gazeau-Klauder (resp.
Klauder-Perelomov) ones. In the fermionic case, the Bargamnn realization leads
to the Klauder-Perelomov coherent states. For each considered realization, the
inner product of two analytic functions is defined in respect to a measure
explicitly computed. The Jacobson generators are realized as differential
operators. It is shown that the obtained coherent states minimize the
Robertson-Schr\"odinger uncertainty relation.
