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arXiv math/06021492006-02math.COmath.AG

4-立方体的超行列式与三角剖分

The Hyperdeterminant and Triangulations of the 4-Cube

Peter Huggins, Bernd Sturmfels, Josephine Yu, Debbie Yuster

备注：: 30 pages, 6 figures; An author's name changed, typos fixed
发表信息：: Mathematics of Computation 77 (2008), no. 263, 1653--1679
DOI：: 10.1090/S0025-5718-08-02073-5

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摘要：

格式为2 x 2 x 2 x 2的超行列式是16个未知数的24次多项式，有2894276项。我们计算这个多项式的牛顿多面体和4-立方体的第二多面体。87959448个正则三角剖分分为25448个D-等价类，每个类对应于牛顿多面体的每个顶点。4-立方体有80876个粗规则的细分，一个次级多面体的每个面，但只有268个来自超行列式。

英文摘要：

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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