# On Cancellative Set Families

* Corresponding author
Abstract : A family of subsets of an $n$-set is $2$-cancellative if, for every four-tuple $\{A, B, C, D\}$ of its members, $A \cup B \cup C=A \cup B \cup D$ implies $C = D$. This generalizes the concept of cancellative set families, defined by the property that $A \cup B \neq A \cup C$ 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 $2^{0.458n}$ to $2^{0.42n}$.
Document type :
Journal articles
Domain :

Cited literature [7 references]

https://hal.archives-ouvertes.fr/hal-00681899
Contributor : Blerina Sinaimeri <>
Submitted on : Thursday, March 22, 2012 - 5:15:56 PM
Last modification on : Monday, August 5, 2019 - 3:00:07 PM
Long-term archiving on: : Monday, November 26, 2012 - 11:56:11 AM

### File

cancellative.pdf
Files produced by the author(s)

### Citation

János Körner, Blerina Sinaimeri. On Cancellative Set Families. Combinatorics, Probability and Computing, Cambridge University Press (CUP), 2007, 16 (5), pp.767-773. ⟨10.1017/S0963548307008413⟩. ⟨hal-00681899⟩

Record views