This paper considers the determination of N‐representability (for diagonal elements) of p‐density matrices restricted to certain finite‐dimensional subspaces of l2 of the configuration space of N identical antisymmetric particles. In particular, an arbitrary set of N + p spin orbitals is selected and one considers the (N+pp)‐dimensional subspace generated by all possible Slater determinants of the spin orbitals being considered. Applying a combinatorial approach to the problem, a necessary and sufficient set of conditions is determined; previous work has dealt only with necessary conditions, except in the 1‐matrix case. The paper concludes by presenting a probabilistic interpretation of these conditions which seems of particular interest for the 2‐matrix case. The conditions presented here in combination with the Pauli principle give a probabilistic view of the expected occupation of p‐tuples of spin orbitals in terms of the expected occupations of lower‐order‐tuples of spin orbitals.
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