DETECTING INTEGRAL POLYHEDRAL FUNCTIONS

Confluentes Mathematici

TYNAN, PHILIP¹  KEDLAYA, KIRAN S¹ 

[1] Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA

关键词: Convex functions;    integral polyhedral functions;    tropical polynomials;   

DOI  :  10.1142/S1793744209000031

学科分类：数学（综合）

来源: World Scientific Publishing Co. Pte. Ltd.

【 摘 要 】

We study the class of real-valued functions on convex subsets of ℝn which are computed by the maximum of finitely many affine functionals with integer slopes. We prove several results to the effect that this property of a function can be detected by sampling on small subsets of the domain. In so doing, we recover in a unified way some prior results of the first author (some joint with Liang Xiao). We also prove that a function on ℝ2 is a tropical polynomial if and only if its restriction to each translate of a generic tropical line is a tropical polynomial.

【 授权许可】

Unknown