The Hyperdeterminant and Triangulations of the 4-Cube

Details The Hyperdeterminant and Triangulations of the 4-Cube The Hyperdeterminant and Triangulations of the 4-Cube

2006-02-08

arxiv.org/abs/math/0602149v2

Mathematics of Computation 77 (2008), no. 263, 1653--1679

Mathematics

Combinatorics

30 pages, 6 figures; An author's name changed, typos fixed

Scientific paper

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.

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