An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions
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Publication:987564
DOI10.1007/s00493-009-2357-xzbMath1212.14005arXivmath/0603256OpenAlexW2058434068WikidataQ57253833 ScholiaQ57253833MaRDI QIDQ987564
Richard Pollack, Saugata Basu, Marie-Françoise Roy
Publication date: 13 August 2010
Published in: Combinatorica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0603256
Modular representations and characters (20C20) Semialgebraic sets and related spaces (14P10) Topology of real algebraic varieties (14P25) Rings and algebras of continuous, differentiable or analytic functions (46E25)
Related Items
VC dimensions of principal component analysis, Refined bounds on the number of connected components of sign conditions on a variety, Bounds of Hausdorff measures of tame sets, VC density of definable families over valued fields
Cites Work
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- Upper bounds for configurations and polytopes in \({\mathbb{R}}^ d\)
- On the number of sets definable by polynomials
- On the homology groups of Stein spaces
- Homology theory for locally compact spaces
- On the number of zero-patterns of a sequence of polynomials
- On the Betti numbers of sign conditions
- There are asymptotically far fewer polytopes than we thought
- Semi-Algebraic Local-Triviality in Semi-Algebraic Mappings
- On the number of cells defined by a family of polynomials on a variety
- Lower Bounds for Approximation by Nonlinear Manifolds
- On the Betti Numbers of Real Varieties
- Algorithms in real algebraic geometry