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比利时vs摩洛哥足彩 ,
university of california san diego

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food for thought seminar

jason o'neill

ucsd

well-separated set systems

abstract:

given a finite set $x$ of size $n$, we can form a metric space on the power set $\mathcal{p}(x)$ by the metric $d(a,b) = |a \triangle b|$ where $a \triangle b := (a \cap b^c) \cup (a^c \cap b)$. an $\alpha$-well separated set system is a subset $\mathcal{f} \subset \mathcal{p}(x)$ so that for all distinct $a, b \in \mathcal{f}$, we have that $d(a,b) \geq \alpha n$. in this talk, we will focus on the case where $\alpha= \frac{1}{2}$ and use linear algebra techniques to explore bounding the size of an $\alpha$-well separated family. we will also discuss the construction of these large $\alpha$-well separated set systems via hadamard matrices.

may 7, 2019

1:00 pm

ap&m 7321

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