PIMS - UVic Discrete Math Seminar: Akina Kuperus

  • Date: 03/23/2023
  • Time: 10:00
Akina Kuperus, University of Victoria

University of Victoria


Keeping up with the Cross-Sperners: An Introduction to Cross-Sperner Systems


A collection of families $(\F_{1}, \F_{2} , \cdots , \F_{k}) \in \mathcal{P}([n])^k$ is \emph{cross-Sperner} if there is no pair $i \not= j$ for which some $F_i \in \F_i$ is comparable to some $F_j \in \F_j$. Two natural measures of the `size' of such a family are the sum $\sum_{i = 1}^k |\F_i|$ and the product $\prod_{i = 1}^k |\F_i|$. We prove upper and lower bounds on the sum measure for general $n$ and $k \ge 2$. In the process, we consider minimizing the number of sets comparable to a family $\F \subseteq \mathcal{P}([n])$ of a given size.

Other Information: 

Location: COR A121

Time: 10am PacificĀ