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Abstract for James B. Shearer, A New Construction for Cancellative Families of Sets 

 Following [2], we say a family, $H$, of subsets of a $n$-element
set is cancellative if $A \cup B = A \cup C$ implies $B =C$ when
$A, B, C \in H$.  We show how to construct cancellative families
of sets with $c 2^{.54797n}$ elements.  This improves the previous
best bound $c 2^{.52832n}$ and falsifies conjectures of Erd\"{o}s
and Katona [3] and Bollob\'{a}s [1].


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