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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
Published electronically: February 4, 2008
MathSciNet review: 2398786
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Abstract: The hyperdeterminant of format $ 2\times 2 \times 2 \times 2$ is a polynomial of degree $ 24$ in $ 16$ unknowns which has $ 2894276$ terms. We compute the Newton polytope of this polynomial and the secondary polytope of the $ 4$-cube. The $ 87959448 $ regular triangulations of the $ 4$-cube are classified into $ 25448$ $ D$-equivalence classes, one for each vertex of the Newton polytope. The $ 4$-cube has $ 80876$ coarsest regular subdivisions, one for each facet of the secondary polytope, but only $ 268$ of them come from the hyperdeterminant.


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Additional Information

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

Debbie S. Yuster
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Address at time of publication: DIMACS Center, Rutgers University, Piscataway, New Jersey 08854
Email: yuster@math.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-08-02073-5
PII: S 0025-5718(08)02073-5
Received by editor(s): February 9, 2006
Received by editor(s) in revised form: January 6, 2007
Published electronically: February 4, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.