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

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math 269 - combinatorics

xing peng

ucsd

on the decomposition of random hypergraphs

abstract:

for an $r$-uniform hypergraph $h$, let $f(h)$ be the minimum number of complete $r$-partite $r$-uniform subhypergraphs of $h$ whose edge sets partition the edge set of $h$. in this talk, i will discuss the value of $f(h)$ for the random hypergraph $h$. namely, i will prove that if $(\log n)^{2.001}/n \leq p \leq 1/2$ and $h \in h^{(r)}(n,p)$, then with high probability $f(h)=(1-\pi(k^{(r-1)}_r)+o(1))\binom{n}{r-1}$, where $\pi(k_{r}^{(r-1)})$ is the tur\'an density of $k_{r}^{(r-1)}$.

june 2, 2015

4:00 pm

ap&m 7321

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