LAUSR

We consider an allocation scheme of $$2n$$ distinguishable particles by $$N$$ different cells under the condition than each cell contains an even number of particles. We show that this scheme is a general allocation scheme defined by the random variable $$\xi_{i}$$ with the distribution $${\mathbf{P}}(\xi_{i}=2k)=\frac{\alpha^{2k}}{(2k)!\cosh\alpha},$$ $$k=0,1,2\dots$$ . Let $$\mu_{2r}(N,K,n)$$ be a number of cells from the first $$K$$ cells that contain $$2r$$ particles. We prove that under some types of convergence of $$n,K,N$$ to infinity $$\mu_{2r}(N,K,n)$$ converges in distribution to the Poisson random variable. The limit Poisson random variable is described.