Oct 8, 2001 · A family of subsets of an n-set is k-locally thin if, for every k-tuple of its members, the ground set has at least one element contained in exactly one of ...
Our proof uses the graph entropy bounding technique to exploit a self-similarity in the structure of the hypergraph associated with such set families. 1.
A family of subsets of an n-set is k-locally thin if, for every k-tuple of its members, the ground set has at least one element contained in exactly one of ...
Oct 22, 2024 · A family of subsets of an n-set is 4-locally thin if for every quadruple of its members the ground set has at least one element contained in ...
The new proof is based on a more careful analysis of the self-similarity of the graph associated with such set families by the graph entropy bounding technique.
For <jats:italic>k</jats:italic> = 5 we derive a new exponential upper bound for the maximum size of these families. This implies the same bound for all odd ...
Feb 22, 2002 · We derive new asymptotic upper bounds for the maximum cardinality of locally thin set families for every even k. This improves on previous ...
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Self-Similarity Bounds for Locally Thin Set Families. A family of subsets of an n-set is k-locally thin if, for every k-tuple of its members, the ground set ...
A family of subsets of an n-set is 4-locally thin if for every quadruple of its members the ground set has at least one element contained in exactly 1 of them.
May 10, 2001 · A family of subsets of an n-set is 4-locally thin if for every quadruple of its members the ground set has at least one element contained in ...