# On splitting and splittable families

@article{Coskey2018OnSA, title={On splitting and splittable families}, author={Samuel Coskey and Bryce Frederickson and Samuel Mathers and Hao-Tong Yan}, journal={arXiv: Combinatorics}, year={2018} }

A set $A$ is said to \emph{split} a finite set $B$ if exactly half the elements of $B$ (up to rounding) are contained in $A$. We study the dual notions: (1) a \emph{splitting family}, a collection of sets such that any subset of $\{1,\ldots,k\}$ is split by a set in the family, and (2) a \emph{splittable family}, a collection of sets such that there is a single set $A$ that splits each set in the family.
We study the minimum size of a splitting family on $\{1,\ldots,k\}$, as well as the… CONTINUE READING

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