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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A combinatorial approach to the diagonal $N$-representability problem
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by Mark Laurance Yoseloff PDF
Trans. Amer. Math. Soc. 190 (1974), 1-41 Request permission


The problem considered is that of the diagonal N-representability of a pth-order reduced density matrix, $p \geq 2$, for a system of N identical fermions or bosons. A finite number M of allowable single particle states is assumed. The problem is divided into three cases, namely: Case I. $M = N + p$ ; Case II. $M < N + p$; Case III. $M > N + p$. Using the theory of polyhedral convex cones, a complete set of necessary and sufficient conditions is first found for Case I. This solution is then employed to find such conditions for Case II. For Case III, two algorithms are developed to generate solutions for the problem, and examples of the usage of these algorithms are given.
    M. Balinski, Ph.D. Thesis, Princeton University, Princeton, N. J., 1959.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 190 (1974), 1-41
  • MSC: Primary 81.47
  • DOI:
  • MathSciNet review: 0337218