Bounding the equivariant Betti numbers of symmetric semi-algebraic sets

DOI10.1016/j.aim.2016.09.015zbMath1423.14331arXiv1312.6582OpenAlexW2962904734MaRDI QIDQ340423

Cordian Riener, Saugata Basu

Publication date: 14 November 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.6582

zbMATH Keywords

symmetric polynomialsequivariant Betti numberssemi-algebraic sets

Mathematics Subject Classification ID

Semialgebraic sets and related spaces (14P10) Topology of real algebraic varieties (14P25)

Related Items (5)

New directions in real algebraic geometry. Abstracts from the workshop held March 19--24, 2023 ⋮ Faster real root decision algorithm for symmetric polynomials ⋮ Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets ⋮ On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms ⋮ Computing critical points for invariant algebraic systems

Cites Work

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• Betti numbers of random real hypersurfaces and determinants of random symmetric matrices
• On the degree and half-degree principle for symmetric polynomials
• On the positivity of symmetric polynomial functions. III: Extremal polynomials of degree 4
• Bounding the Betti numbers and computing the Euler-Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials
• Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials
• Inequalities defining orbit spaces
• Positive symmetric functions
• On the Betti numbers of semialgebraic sets defined by few quadratic inequalities
• On the positivity of symmetric polynomial functions. I: General results
• On the positivity of symmetric polynomial functions. II: Lattice general results and positivity criteria for degrees 4 and 5
• Lower bounds for arithmetic networks. II: Sum of Betti numbers
• FI-modules and stability for representations of symmetric groups
• Feasibility testing for systems of real quadratic equations
• A note on extrema of linear combinations of elementary symmetric functions
• Quotients of Coxeter complexes and 𝑃-partitions
• Linear Decision Trees, Subspace Arrangements, and Mobius Functions
• BETTI NUMBERS OF SEMIALGEBRAIC AND SUB-PFAFFIAN SETS
• On a theory of computation and complexity over the real numbers: 𝑁𝑃- completeness, recursive functions and universal machines
• Approximation of definable sets by compact families, and upper bounds on homotopy and homology
• Most Tensor Problems Are NP-Hard
• On the Betti Numbers of Real Varieties
• Decision tree complexity and Betti numbers
• Algorithms in real algebraic geometry

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