Fractional statistics in terms of the r-generalized Fibonacci sequences

摘要

We develop a method to approach quantum gases of quasiparticles with generalized statistics. This way is based on Fibonacci hierarchies and offers an alternative issue to the Haldane-Wu method. We give the statistical weights densities pm of gases of quasiparticles with s = 1/M : mod(1), M greater than or equal to 2, using the combinatorial aspects of M-generalized Fibonacci series. This is a remarkable feature which envelopes naturally the Fermi and Bose statistics. [References: 32]