On nearest neighbor degeneracies of indistinguishable particles

Abstract

Arrangement degeneracies suggested by sufficient statistics associated with binary stationary mth order Markov chains are discussed, and are shown to correspond and generalize some degeneracies arising when indistinguishable particles are placed on a one-dimensional lattice with n compartments. From these statistics it is possible to define an mth order unit. The arrangement degeneracy obtained from s 1’s and n−s 0’s so that lower order units are placed in higher order is difficult. For this case only the third order arrangement degeneracy is obtained, the first and second orders being relatively simple. These results are applied in determining the asymptotic distributions of rare events.