On the normalization of one-dimensional lattice statistics
Richmond B. McQuistan · Journal of Mathematical Physics · 1978
It is shown that the normalization of the statistics associated with the distribution of λ-bell particles [λ=1 for simple particles; λ=2 for dumbbell particles, etc.] on a one-dimensional lattice space, is given by a simple, two-term recursion relation. This normalization, for a lattice consisting of N sites, is shown to be (1/x+)N, where x+ is the real positive root of the equation xλ +x−1=0. A general recursion expression is also developed that describes the higher order moments of the statistics.