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From a geometric point of view, Pauli's exclusion principle defines a hypersimplex.
Wolfgang Pauli, Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren , Z. Phys. 31
1925
Earlier work this paper cites.
Paul A. M. Dirac, Note on exchange phenomena in the thomas atom , Math. Proc. Cambridge Philos. Soc. 26
1930
Earlier work this paper cites.
Satosi Watanabe, Über die anwendung thermodynamischer begriffe auf den normalzustand des atomkern , Z. Physik 113
1939
Earlier work this paper cites.
Kôdi Husimi, Some formal properties of the density matrix , Proc. Phys. Math. Soc. Japan 22
1940
Earlier work this paper cites.
Godfrey H. Hardy, John E. Littlewood, and George Pólya, Inequalities , Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1988, Reprint of the 1952 edition
1952
Earlier work this paper cites.
Richard Rado, An inequality , J. London Math. Soc. 27
1952
Earlier work this paper cites.
Per-Olov Löwdin, Quantum theory of many-particle systems. I. Physical interpretations by means of density matrices, natural spin-orbitals, and convergence problems in the method of configurational interaction , Phys. Rev. (2) 97
1955
Earlier work this paper cites.
Robert U. Ayres, Variational approach to the many-body problem , Phys. Rev. 111
1958
Earlier work this paper cites.
Charles A. Coulson, Present state of molecular structure calculations , Rev. Mod. Phys. 32
1960
Earlier work this paper cites.
Harold W. Kuhn, Linear inequalities and the Pauli principle , Proc. Sympos. Appl. Math., Vol. 10, American Mathematical Society, Providence, R.I., 1960, pp. 141–147
1960
Earlier work this paper cites.
Leonid Mirsky, Results and problems in the theory of doubly-stochastic matrices , Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 1
1962
Earlier work this paper cites.
Chen Ning Yang, Concept of off-diagonal long-range order and the quantum phases of liquid He and of superconductors , Rev. Modern Phys. 34
1962
Earlier work this paper cites.
Albert John Coleman, Structure of fermion density matrices , Rev. Modern Phys. 35
1963
Earlier work this paper cites.
Claude Garrod and Jerome K. Percus, Reduction of the N N -particle variational problem , J. Math. Phys. 5
1964
Earlier work this paper cites.
David Gale, Optimal assignments in an ordered set: An application of matroid theory , J. Combinatorial Theory 4
1968
Earlier work this paper cites.
R. E. Borland and K. Dennis, The conditions on the one-matrix for three-body fermion wavefunctions with one-rank equal to six , J. Phys. B 5
1972
Earlier work this paper cites.
by same author, Necessary conditions for N N -representability of reduced density matrices , J. Math. Phys. 13
1972
Earlier work this paper cites.
Bertram Kostant, On convexity, the Weyl group and the Iwasawa decomposition , Ann. Sci. École Norm. Sup. (4) 6
1974
Earlier work this paper cites.
Andrei M. Gabrièlov, Israil M. Gelfand, and Mark V. Losik, Combinatorial computation of characteristic classes. I, II , Funkcional. Anal. i Priložen. 9
1975
Earlier work this paper cites.
László Babai, Symmetry groups of vertex-transitive polytopes , Geom. Dedicata 6
1977
Earlier work this paper cites.
by same author, Convex structure of electrons , Int. J. Quant. Chem. 11
1977
Earlier work this paper cites.
Jean-Pierre Serre, Linear representations of finite groups , vol. 42, Springer, 1977
1977
Earlier work this paper cites.
Richard P. Stanley, Cohen-Macaulay complexes , Higher combinatorics (Proc. NATO Advanced Study Inst., Berlin, 1976), D. Reidel Publishing Co., Dordrecht-Boston, Mass., 1977, pp. 51–62
1977
Earlier work this paper cites.
Mel Levy, Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem , Proc. Natl. Acad. Sci. U.S.A 76
1979
Earlier work this paper cites.
Steven M. Valone, Consequences of extending 1-matrix energy functionals from pure–state representable to all ensemble representable 1-matrices , J. Chem. Phys. 73
1980
Earlier work this paper cites.
Michael F. Atiyah, Convexity and commuting Hamiltonians , Bull. London Math. Soc. 14
1982
Earlier work this paper cites.
Victor Guillemin and Shlomo Sternberg, Convexity properties of the moment mapping , Invent. Math. 67
1982
Earlier work this paper cites.
Elliot H. Lieb, Density functionals for coulomb systems , Int. J. Quantum Chem. 24
1983
Earlier work this paper cites.
Frances Kirwan, Convexity properties of the moment mapping. III , Invent. Math. 77
1984
Earlier work this paper cites.
Alexander Schrijver, Theory of linear and integer programming , Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons, 1986
1986
Earlier work this paper cites.
Robert Erdahl and Vedene H. Smith (eds.), Density matrices and density functionals: proceedings of the a. john coleman symposium , Dordrecht, Springer, Dordrecht, 1987
1987
Earlier work this paper cites.
Israil M. Gelfand, Robert Mark Goresky, Robert D. MacPherson, and Vera V. Serganova, Combinatorial geometries, convex polyhedra, and Schubert cells , Adv. Math. 63
1987
Earlier work this paper cites.
Eberhard K. U. Gross, Luiz N. Oliveira, and Walter Kohn, Rayleigh-Ritz variational principle for ensembles of fractionally occupied states , Phys. Rev. A (3) 37
1988
Earlier work this paper cites.
James E. Humphreys, Reflection groups and Coxeter groups , Cambridge Studies in Advanced Mathematics, vol. 29, Cambridge University Press, Cambridge, 1990
1990
Earlier work this paper cites.
David Avis and Komei Fukuda, A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra , Discrete Comput. Geom. 8
1992
Earlier work this paper cites.
Louis J. Billera and Bernd Sturmfels, Fiber polytopes , Ann. of Math. (2) 135
1992
Earlier work this paper cites.
Shmuel Onn, Geometry, complexity, and combinatorics of permutation polytopes , J. Combin. Theory Ser. A 64
1993
Earlier work this paper cites.
Louis J. Billera, Mikhail M. Kapranov, and Bernd Sturmfels, Cellular strings on polytopes , Proc. Amer. Math. Soc. 122
1994
Earlier work this paper cites.
National Research Council, Mathematical challenges from theoretical/computational chemistry , The National Academies Press, Washington, DC, 1995
1995
Cited alongside, same era.
Günter M. Ziegler, Lectures on polytopes , GTM, vol. 152, Springer-Verlag, New York, 1995
1995
Cited alongside, same era.
Herbert Edelsbrunner, Pavel Valtr, and Emo Welzl, Cutting dense point sets in half , Discrete Comput. Geom. 17
1997
Cited alongside, same era.
William Fulton, Young tableaux , London Mathematical Society Student Texts, vol. 35, Cambridge University Press, Cambridge, 1997
1997
Cited alongside, same era.
Ralph T. Rockafellar, Convex analysis , Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997
1997
Cited alongside, same era.
Caroline J. Klivans and Vic Reiner, Shifted set families, degree sequences, and plethysm , Electron. J. Combin. 15
2008
Later among the works it cites.
2009
Later among the works it cites.
Alexander Postnikov, Permutohedra, associahedra, and beyond , Int. Math. Res. Not. IMRN (2009), no. 6, 1026–1106
2009
Later among the works it cites.
Nicolas Ressayre, Geometric invariant theory and the generalized eigenvalue problem , Invent. Math. 180
2010
Later among the works it cites.
Albert W. Marshall, Ingram Olkin, and Barry C. Arnold, Inequalities: theory of majorization and its applications , second ed., Springer Series in Statistics, Springer, New York, 2011
2011
Later among the works it cites.
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Egon Schulte, Symmetry of polytopes and polyhedra , Handbook of discrete and computational geometry, CRC Press Ser. Discrete Math. Appl., CRC, Boca Raton, FL, 1997, pp. 311–330
1997
Cited alongside, same era.
Alexander A. Klyachko, Stable bundles, representation theory and Hermitian operators , Selecta Math. (N.S.) 4
1998
Cited alongside, same era.
Michel Brion, On the general faces of the moment polytope , Int. Math. Res. Not. IMRN 1999
1999
Cited alongside, same era.
Victor Reiner, The generalized Baues problem , New perspectives in algebraic combinatorics (Berkeley, CA, 1996–97), Math. Sci. Res. Inst. Publ., vol. 38, Cambridge Univ. Press, Cambridge, 1999, pp. 293–336
1999
Cited alongside, same era.
Arkady Berenstein and Reyer Sjamaar, Coadjoint orbits, moment polytopes, and the Hilbert-Mumford criterion , J. Amer. Math. Soc. 13
2000
Cited alongside, same era.
Jerzy Cioslowski (ed.), Many-electron densities and reduced density matrices , Mathematical and Computational Chemistry, Springer, US, 2000
2000
Cited alongside, same era.
Albert John Coleman and Vyacheslav I. Yukalov, Reduced density matrices , Lecture Notes in Chemistry, vol. 72, Springer-Verlag, Berlin, 2000, Coulson’s challenge
2000
Cited alongside, same era.
Raman Sanyal, Frank Sottile, and Bernd Sturmfels, Orbitopes , Mathematika 57
2011
Later among the works it cites.
Jianxin Chen, Zhengfeng Ji, Mary Beth Ruskai, Bei Zeng, and Duan-Lu Zhou, Comment on some results of Erdahl and the convex structure of reduced density matrices , J. Math. Phys. 53
2012
Later among the works it cites.
by same author, Structure of fermionic density matrices: Complete n n -representability conditions , Phys. Rev. Lett. 108
2012
Later among the works it cites.
by same author, Enumerative combinatorics. Volume 1 , second ed., Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge, 2012
2012
Later among the works it cites.
Paul H. Edelman, Tatiana Gvozdeva, and Arkadii Slinko, Simplicial complexes obtained from qualitative probability orders , SIAM J. Discrete Math. 27
2013
Later among the works it cites.
Brian C. Hall, Quantum theory for mathematicians , GTM, vol. 267, Springer, New York, 2013
2013
Later among the works it cites.
Christian Schilling, David Gross, and Matthias Christandl, Pinning of fermionic occupation numbers , Phys. Rev. Lett. 110
2013
Later among the works it cites.
Achill Schürmann, Exploiting symmetries in polyhedral computations , Discrete geometry and optimization, Fields Inst. Commun., vol. 69, Springer, New York, 2013, pp. 265–278
2013
Later among the works it cites.
Michael Walter, Multipartite quantum states and their marginals , Ph.D. thesis, ETH Zürich, Zürich, 2014, pp. xi+201
2014
Later among the works it cites.
Christian Schilling, The quantum marginal problem , Mathematical results in quantum mechanics, World Sci. Publ., Hackensack, NJ, 2015, pp. 165–176
2015
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by same author, Valid orderings of real hyperplane arrangements , Discrete Comput. Geom. 53
2015
Later among the works it cites.
Nima Arkani-Hamed, Jacob Bourjaily, Freddy Cachazo, Alexander Goncharov, Alexander Postnikov, and Jaroslav Trnka, Grassmannian geometry of scattering amplitudes , Cambridge University Press, Cambridge, 2016
2016
Later among the works it cites.
Winfried Bruns, Bogdan Ichim, and Christof Söger, The power of pyramid decomposition in Normaliz , J. Symbolic Comput. 74
2016
Later among the works it cites.
Erik Friese and Frieder Ladisch, Affine symmetries of orbit polytopes , Adv. Math. 288
2016
Later among the works it cites.
Nicholas Matteo, Combinatorially two-orbit convex polytopes , Discrete Comput. Geom. 55
2016
Later among the works it cites.
by same author, Pure- n n -representability conditions of two-fermion reduced density matrices , Phys. Rev. A 94
2016
Later among the works it cites.
Klaas Landsman, Foundations of quantum theory , Fundamental Theories of Physics, vol. 188, Springer, Cham, 2017
2017
Later among the works it cites.
Tomasz Maciążek and Valdemar Tsanov, Quantum marginals from pure doubly excited states , J. Phys. A 50
2017
Later among the works it cites.
Christian Schilling, Murat Altunbulak, Stefan Knecht, Alexandre Lopes, James D. Whitfield, Matthias Christandl, David Gross, and Markus Reiher, Generalized Pauli constraints in small atoms , Phys. Rev. A 97
2018
Later among the works it cites.
Volker Bach and Robert Rauch, Orthogonalization of fermion k k -body operators and representability , Phys. Rev. A 99
2019
Later among the works it cites.
Federico Ardila, Federico Castillo, Christopher Eur, and Alexander Postnikov, Coxeter submodular functions and deformations of Coxeter permutahedra , Adv. Math. 365
2020
Later among the works it cites.
2020
Later among the works it cites.
2020
Later among the works it cites.
2020
Later among the works it cites.
2020
Later among the works it cites.
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2021
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2021
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2021
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