Fermionic relatives of Stirling and Lah numbers

Abstract

In this paper certain 'fermionic' Stirling numbers introduced recently are discussed. Roughly speaking, these numbers are obtained by taking the 'fermionic' limit q → −1 of the q-deformed Stirling numbers. The usual Stirling numbers correspond in this language to the 'bosonic' limit q → 1. It is shown that the fermionic Stirling numbers are given by binomial coefficients and that they satisfy the same relations as the undeformed Stirling numbers. The fermionic relatives of Lah numbers are also very briefly discussed.