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X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20240101T000000
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DTSTART;TZID=Asia/Seoul:20250318T163000
DTEND;TZID=Asia/Seoul:20250318T173000
DTSTAMP:20260417T071652
CREATED:20250205T073256Z
LAST-MODIFIED:20250305T204931Z
UID:10539-1742315400-1742319000@dimag.ibs.re.kr
SUMMARY:Michał Seweryn\, Dimension and standard examples in planar posets
DESCRIPTION:The dimension of a poset is the least integer $d$ such that the poset is isomorphic to a subposet of the product of $d$ linear orders. In 1983\, Kelly constructed planar posets of arbitrarily large dimension. Crucially\, the posets in his construction involve large standard examples\, the canonical structure preventing a poset from having small dimension. Kelly’s construction inspired one of the most challenging questions in dimension theory: are large standard examples unavoidable in planar posets of large dimension? We answer the question affirmatively by proving that every $d$-dimensional planar poset contains a standard example of order $\Omega(d)$. More generally\, we prove that every poset from Kelly’s construction appears in every poset with a planar cover graph of sufficiently large dimension. \njoint work with Heather Smith Blake\, Jędrzej Hodor\, Piotr Micek\, and William T. Trotter.
URL:https://dimag.ibs.re.kr/event/2025-03-18/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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