Mathematics of Computation

Author(s): Peter Huggins; Bernd Sturmfels; Josephine Yu; Debbie S. Yuster.
Journal: Math. Comp. 77 (2008), 1653-1679.
MSC (2000): Primary 52B55; Secondary 68W30
Posted: February 4, 2008
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Abstract: The hyperdeterminant of format $2\times 2 \times 2 \times 2$ is a polynomial of degree

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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Peter Huggins
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: phuggins@math.berkeley.edu

Bernd Sturmfels
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: bernd@math.berkeley.edu

Josephine Yu
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Address at time of publication: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: jyu@math.mit.edu

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