Exploring implications of trace (inversion) formula and Artin algebras in extremal combinatorics

DOI10.1007/s00200-023-00619-1zbMath1530.05195OpenAlexW4385779075MaRDI QIDQ6139280

Luis Miguel Pardo

Publication date: 18 January 2024

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00200-023-00619-1

zbMATH Keywords

VC dimensionSauer-Shelah-Perles lemmazero-dimensional algebrastrace inversion formula

Mathematics Subject Classification ID

Extremal set theory (05D05) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Combinatorial aspects of groups and algebras (05E16)

Cites Work

• Definability and fast quantifier elimination in algebraically closed fields
• On the density of sets of vectors
• On the trace of finite sets
• On the number of sets in a null t-design
• On the vector space of 0-configurations
• Defect Sauer results
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• Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory
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• On the density of families of sets
• On the size of Kakeya sets in finite fields
• Combinatorial Nullstellensatz
• Shattered Sets and the Hilbert Function
• On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
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