A combinatoric result related to the N‐body problem Available to Purchase

In the set of complete chains of partitions of N objects, let chains that are related through a permutation of the objects be termed equivalent. The number of equivalence classes μ_N is shown to equal the Euler number ‖E_N−1‖ if N is odd, and 2^N(2^N−1)‖B_N‖/N, where B_N is a Bernoulli number, if N is even. The number of elements in each class is also found. In the Yakubovskii‐type formulation of the N‐body problem in quantum mechanics, μ_N is the basic number of coupled equations when all particles are identical.