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The hypersimplex $\Delta_{k+1,n}$ is the image of the positive Grassmannian $Gr^{\geq 0}_{k+1,n}$ under the moment map.
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Constantin Carathéodory · 1911
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I. M. Gelfand, R. M. Goresky, R. D. MacPherson, and V. V. Serganova · 1987
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Bernd Sturmfels · 1988
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