q-fermionic numbers and their roles in some physical problems

Abstract 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.