On the universal partition theorem for 4-polytopes
type: Item
instance of: scholarly article
title: On the universal partition theorem for 4-polytopes
zbMATH Open document ID: 0914.52004
DOI: 10.1007/PL00009367
author: D. Massart
published in: Discrete \& Computational Geometry
publication date: 1999-06-21T00:00:00Z
review text: Every semialgebraic stratification of \(\mathbb{R}^n\) (defined over \(\mathbb{Z})\) is ,``stably equivalent'' to the family of realization spaces of an effectively computable set of \(4\)-dimensional polytopes. This ``universal partition theorem for \(4\)-dimensional polytopes'' was first established by \textit{J. Richter-Gebert} [see: `Realization spaces of polytopes', Springer LVM Vol. 1643 (1996; Zbl 0866.52009)] who also provided the ``right'' concept of stable equivalence. The new (mostly independent) development and proof of the universal partition theorem for \(4\)-po1ytopes by H. Günzel has several new elements and components. In particular, it provides a substantially more restrictive normal form for the straight-line programs that compute semialgebraic sets/families; furthermore, the ``von Staudt polytopes'' introduced here give a very compact encoding of such normal forms into the combinatorics of \(4\)-polytopes.
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 52B40
Mathematics Subject Classification ID: 14P10
Mathematics Subject Classification ID: 51A25
zbMATH DE Number: 1164316
zbMATH Keywords: convex polytope
zbMATH Keywords: realization space
zbMATH Keywords: semialgebraic set
zbMATH Keywords: stable equivalence
zbMATH Keywords: von Staudt construction
zbMATH Keywords: 4-polytope
zbMATH Keywords: universality theorem
zbMATH Keywords: universal partition theorem
reviewed by: Günter M. Ziegler
MaRDI profile type: Publication
full work available at URL: pl00009367
OpenAlex ID: W2022806840
description: scientific article; zbMATH DE number 1164316