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SUMMARY:Alexander Sidorenko (Rényi Institute of Mathematics)
DTSTART:20210405T140000Z
DTEND:20210405T150000Z
DTSTAMP:20260423T052448Z
UID:EPC/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/53/">On 
 the asymptotic behavior of the classical Turán numbers</a>\nby Alexander 
 Sidorenko (Rényi Institute of Mathematics) as part of Extremal and probab
 ilistic combinatorics webinar\n\n\nAbstract\nA subset of vertices in a hyp
 ergraph H is called independent if it does not contain an edge of $H$. The
  independence number $\\alpha(H)$ is the size of the largest independent s
 et. The classical Turán number $T(n\,\\alpha+1\,r)$ is the minimum number
  of edges in an $n$-vertex $r$-uniform hypergraph $H$ with $\\alpha(H) \\l
 e \\alpha$. In other words\, $\\binom{n}{r} - T(n\,k\,r)$ is the largest n
 umber of edges in an $n$-vertex $r$-uniform hypergraph that does not conta
 in a complete k-vertex subgraph.\n\nThe limit of $T(n\,k\,r) / \\binom{n}{
 r}$ with $n\\to\\infty$ is known as Turán density $t(k\,r)$. Pál Turán 
 in 1941 proved that $t(\\alpha+1\,2) = 1/\\alpha$. It is widely believed t
 hat $t(\\alpha+1\,3) = 4/\\alpha^2$. I will discuss the asymptotic behavio
 r of $t(k\,r)$ in respect to $k$ and $r$. I will also cover similar topics
  for the codegree Turán problem.\n
LOCATION:https://researchseminars.org/talk/EPC/53/
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