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On Cancellative Set Families

Published online by Cambridge University Press:  01 September 2007

JÁNOS KÖRNER  and
BLERINA SINAIMERI
JÁNOS KÖRNER
Affiliation:
Department of Computer Science, Università ‘La Sapienza’, via Salaria 113, 00198 Roma, Italy (e-mail: korner@di.uniroma1.it, sinaimeri@di.uniroma1.it)
BLERINA SINAIMERI
Affiliation:
Department of Computer Science, Università ‘La Sapienza’, via Salaria 113, 00198 Roma, Italy (e-mail: korner@di.uniroma1.it, sinaimeri@di.uniroma1.it)
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Abstract

A family of subsets of an n-set is 2-cancellative if, for every four-tuple {A, B, C, D} of its members, A∪ B∪C=A∪ B∪ D implies C = D. This generalizes the concept of cancellative set families, defined by the property that A∪B ≠A ∪ C for A, B, C all different. The asymptotics of the maximum size of cancellative families of subsets of an n-set is known (Tolhuizen [7]). We provide a new upper bound on the size of 2-cancellative families, improving the previous bound of 20.458n to 20.42n.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 5 , September 2007 , pp. 767 - 773
Copyright
Copyright © Cambridge University Press 2007

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References

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