Polytropes and Tropical Eigenspaces: Cones of Linearity

被引：4

作者：

Ngoc Mai Tran ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Stat, Berkeley, CA 94720 USA

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2014年 / 51卷 / 03期

关键词：

Polytrope; Tropical algebra; Eigenspace; Combinatorial type; All-pairs shortest path;

D O I：

10.1007/s00454-014-9574-9

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The map which takes a square matrix A to its polytrope is piecewise linear. We show that cones of linearity of this map form a polytopal fan partition of , whose face lattice is anti-isomorphic to the lattice of complete set of connected relations. This fan refines the non-fan partition of corresponding to cones of linearity of the eigenvector map. Our results answer open questions in a previous work with Sturmfels (Bull. Lond. Math. Soc. 54:27-36, 2013) and lead to a new combinatorial classification of polytropes and tropical eigenspaces.

引用

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页码：539 / 558

页数：20

共 19 条

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