The Hyperdeterminant and Triangulations of the 4-Cube
Combinatorics
2015-06-26 v2 Algebraic Geometry
Abstract
The hyperdeterminant of format 2 x 2 x 2 x 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.
Cite
@article{arxiv.math/0602149,
title = {The Hyperdeterminant and Triangulations of the 4-Cube},
author = {Peter Huggins and Bernd Sturmfels and Josephine Yu and Debbie Yuster},
journal= {arXiv preprint arXiv:math/0602149},
year = {2015}
}
Comments
30 pages, 6 figures; An author's name changed, typos fixed