q-deformed fermion oscillators, zero-point energy and inclusion-exclusion principle

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 $q \to 1$. 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.