On Cancellative Set Families

János Körner (1) , Blerina Sinaimeri (1)

1 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]

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 $2^{0.42n}$.

Domaines: Mathématique discrète [cs.DM]; Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

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