Self-Similarity Bounds for Locally Thin Set Families

Authors:
Emanuela Fachini;János Körner;Angelo Monti
Affiliations:
Department of Computer Science, University of Rome I ‘La Sapienza’, Via Salaria 113, 00198 Roma, Italy (e-mail: fachini, korner, monti@dsi.uniroma1.it);Department of Computer Science, University of Rome I ‘La Sapienza’, Via Salaria 113, 00198 Roma, Italy (e-mail: fachini, korner, monti@dsi.uniroma1.it);Department of Computer Science, University of Rome I ‘La Sapienza’, Via Salaria 113, 00198 Roma, Italy (e-mail: fachini, korner, monti@dsi.uniroma1.it)
Venue:
Combinatorics, Probability and Computing
Year:
2001

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Abstract

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 them. For k = 5 we derive a new exponential upper bound for the maximum size of these families. This implies the same bound for all odd values of k 3. Our proof uses the graph entropy bounding technique to exploit a self-similarity in the structure of the hypergraph associated with such set families.