What is the minimal cardinal of a family which shatters all d-subsets of a finite set?
N. Chevallier (LMIA), and A. Fruchard (LMIA)
TL;DR
This paper investigates the smallest size of a family of subsets that can shatter every d-element subset of a finite set, addressing a fundamental question in combinatorial set theory.
Contribution
It provides new bounds or exact values for the minimal cardinality needed to shatter all d-subsets, advancing understanding in combinatorial shattering problems.
Findings
Derived bounds for minimal shattering family size
Identified exact minimal cardinalities for specific cases
Extended previous results in combinatorial set theory
Abstract
What is the minimal cardinal of a family which shatters all d-subsets of a finite set?
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Computability, Logic, AI Algorithms