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Generalized fermion algebra

A one-parameter generalized fermion algebra ${\cal B}_κ(1)$ is introduced. The Fock representation is studied. The associated coherent states are constructed and the polynomial representation, in the Bargmann sense, is derived. A special attention is devoted to the limiting case $κ\rightarrow 0$ where the fermionic coherent states, labeled by Grassmann variables, are obtained. The physical relevance of the algebra is illustrated throughout Calogero-Sutherland system.