Betti numbers of polynomial hierarchical models for experimental designs

DOI10.1007/s10472-012-9295-9zbMath1286.13028OpenAlexW1968508854WikidataQ60246142 ScholiaQ60246142MaRDI QIDQ1926583

Eduardo Sáenz-de-Cabezón, Hugo Maruri-Aguilar, Henry P. Wynn

Publication date: 28 December 2012

Published in: Annals of Mathematics and Artificial Intelligence (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10472-012-9295-9

zbMATH Keywords

Hilbert functionBetti numbersexperimental designGröbner fan

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Syzygies, resolutions, complexes and commutative rings (13D02) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Related Items (5)

Structure indicators for transportation graph analysis. I: Planar connected simple graphs ⋮ Alexander duality in experimental designs ⋮ Sensitivity analysis of discrete preference functions using Koszul simplicial complexes ⋮ Topological techniques in model selection ⋮ Two-factor saturated designs: cycles, Gini index, and state polytopes

Uses Software

• CoCoA
• Macaulay2
• SINGULAR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Gröbner fan of an ideal
• Standard bases and geometric invariant theory. I: Initial ideals and state polytopes
• On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets
• Corner cuts and their polytopes
• The Hilbert zonotope and a polynomial time algorithm for universal Gröbner bases.
• The number of plane corner cuts
• On the number of corner cuts
• Betti numbers of Stanley-Reisner rings determine hierarchical Markov degrees
• Interpretation of interaction: a review
• Minimal average degree aberration and the state polytope for experimental designs
• Generalised confounding with Grobner bases
• Combinatorial Commutative Algebra
• Level Algebras, Lex Segments, and Minimal Hilbert Functions
• SINGULAR
• Upper bounds for the betti numbers of a given hilbert function
• Maximum betti numbers of homogeneous ideals with a given hilbert function
• Additive and multiplicative models for the joint effect of two risk factors
• Linear Transformations in Boolean Complexity Theory
• On the Betti Numbers of Real Varieties
• Cutting corners

This page was built for publication: Betti numbers of polynomial hierarchical models for experimental designs