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Shattering-Extremal Systems

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arxiv 1211.2980 v1 pith:SMNKNHDC submitted 2012-11-13 math.CO cs.CGcs.DMcs.LG

Shay Moran This is my paper · ORCID
classification math.COcs.CGcs.DMcs.LG
keywords systemsstructureapplicationsbeencharacterizationscombinatoricscomputationalconcepts
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The Shatters relation and the VC dimension have been investigated since the early seventies. These concepts have found numerous applications in statistics, combinatorics, learning theory and computational geometry. Shattering extremal systems are set-systems with a very rich structure and many different characterizations. The goal of this thesis is to elaborate on the structure of these systems.

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  1. Ample sets in Cartesian products

    math.CO 2026-07 accept novelty 7.0 of 10

    Ample sets of Cartesian products are characterized by shattering-to-strong-shattering of minor-subproducts and inherit the main binary-case equivalences plus contractible prism complexes.

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