q-Fermionic Numbers and Their Roles in Some Physical Problems

The q-fermion numbers emerging from the q-fermion oscillator algebra are used to reproduce the q-fermionic Stirling and Bell numbers. New recurrence relations for the expansion coefficients in the 'anti-normal ordering' of the q-fermion operators are derived. The roles of the q-fermion numbers in q-stochastic point processes and the Bargmann space representation for q-fermion operators are explored.