The hyperdeterminant and triangulations of the 4-cube
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- by Peter Huggins, Bernd Sturmfels, Josephine Yu and Debbie S. Yuster PDF
- Math. Comp. 77 (2008), 1653-1679 Request permission
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.References
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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
- MR Author ID: 238151
- 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
- Received by editor(s): February 9, 2006
- Received by editor(s) in revised form: January 6, 2007
- Published electronically: February 4, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 77 (2008), 1653-1679
- MSC (2000): Primary 52B55; Secondary 68W30
- DOI: https://doi.org/10.1090/S0025-5718-08-02073-5
- MathSciNet review: 2398786