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UID:2026100603273320261005T15000020261005T1600006ac46aa5d408c@uic.edu
CATEGORIES:MEETING
STATUS:TENTATIVE
DTSTAMP:20261005T110811Z
DTSTART:20261005T150000
DTEND:20261005T160000
SUMMARY:Mathematical Computer Science Seminar: Extremal hypergraphs without generalized $4$-cycles\, by Jie Ma
DESCRIPTION:Jie Ma\, Tsinghua University: Extremal hypergraphs without generalized $4$-cycles          In 1977\, ErdH{o}s posed the problem of determining the maximum number $f_r(n)$ of edges in an $n$-vertex $r$-uniform hypergraph in which all disjoint pairs of edges have distinct unions.&#013\; F"uredi later conjectured that\, for every fixed $rge 4$ and all sufficiently large $n$\, $f_r(n)=binom{n-1}{r-1}+lfloor frac{n-1}{r}rfloor$.  &#013\; In this paper\, we prove this conjecture and determine all extremal configurations.  &#013\; Our proof combines a stability theorem for such dense hypergraphs with a delicate deletion argument applied to an associated bipartite $3$-graph.&#013\; The stability theorem also resolves a conjecture of Mubayi.      update this event | Event post: https://mscs.uic.edu/events?page_id=5202515
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