Fermionic relatives of Stirling and Lah numbers

A Comparative Study on q-Deformed Fermion Oscillators

“…Moreover, both the PVC-and the VPJC-oscillator algebras could be used to study fractional statistics due to their unusual Fock space representation properties, i. e. it is possible to occupy more than two q-fermions in a given quantum state. Also, the virial coefficients in (14) and (22) do not depend on the deformation parameter q. This situation contrasts with the results of [41][42][43][44], where a quantum group covariant twoparameter deformed fermion gas was considered, and the virial coefficients were expressed in terms of the two independent real deformation parameters.…”

A new combinatorial interpretation of a $q$-analogue of the Lah numbers

“…with the initial conditions L(n, 0) = δ n,0 and L(0, k) = δ 0,k ∀n, k ∈ N. The numbers L(n, k) are called Lah numbers, after Ivo Lah [5], who introduced them as the connection constants in the polynomial identities For applications to physics, see, e.g., [9] and [10] and the references therein, and see Section 3.3 of [6] for a related sequence of linear differential equations.…”

REMOVED: On q-deformed Stirling numbers☆

“…The fermionic Stirling numbers of the first and second kind are denoted by s f (n, k), S f (n, k), respectively. In this paper, we use notation in the work of Kim [9] and Schork [20]. q-Stirling numbers were first defined in the work of Carlitz [1].…”