Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

The hyperdeterminant and triangulations of the 4-cube

Authors: Peter Huggins, Bernd Sturmfels, Josephine Yu and Debbie S. Yuster
Journal: Math. Comp. 77 (2008), 1653-1679
MSC (2000): Primary 52B55; Secondary 68W30
Posted: February 4, 2008
MathSciNet review: 2398786
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Abstract | References | Similar Articles | Additional Information

Abstract: The hyperdeterminant of format $2\times 2 \times 2 \times 2$ is a polynomial of degree in unknowns which has terms. We compute the Newton polytope of this polynomial and the secondary polytope of the -cube. The regular triangulations of the -cube are classified into -equivalence classes, one for each vertex of the Newton polytope. The -cube has coarsest regular subdivisions, one for each facet of the secondary polytope, but only of them come from the hyperdeterminant.

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