The theory of Fermion oscillators has two essential ingredients: zero-point
energy and Pauli exclusion principle. We devlop the theory of the statistical
mechanics of generalized q-deformed Fermion oscillator algebra with inclusion
principle (i.e., without the exclusion principle), which corresponds to
ordinary fermions with Pauli exclusion principle in the classical limit qβ1. Some of the remarkable properties of this theory play a crucial role in the
understanding of the q-deformed Fermions. We show that if we insist on the weak
exclusion principle, then the theory has the expected low temperature limit as
well as the correct classical q-limit.Comment: 10 pages, Latex, submitted to Physical Review