Representing simple d-dimensional polytopes by d polynomials

• 成果类型: Article
• 署名作者: Averkov, Gennadiy; Henk, Martin
• 署名单位: Otto von Guericke University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-009-0280-y
• 发表日期: 2011
• 页码: 203-230
• 关键词: INEQUALITIES

摘要

A polynomial representation of a convex d-polytope P is a finite set {p(1)(x), ... , p(n)(x)} of polynomials over R-d such that P = {x is an element of R-d : p(i)(x) >= 0 for every 1 <= i <= n}. Let s(d, P) be the least possible n as above. It is conjectured that s(d, P) = d for all convex d-polytopes P. We confirm this conjecture for simple d-polytopes by providing an explicit construction of d polynomials that represent a given simple d-polytope P.