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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:20230101T000000
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DTSTART;TZID=Asia/Seoul:20240111T163000
DTEND;TZID=Asia/Seoul:20240111T173000
DTSTAMP:20260417T010427
CREATED:20231116T155919Z
LAST-MODIFIED:20240705T155117Z
UID:7919-1704990600-1704994200@dimag.ibs.re.kr
SUMMARY:Jinyoung Park (박진영)\, Dedekind's Problem and beyond
DESCRIPTION:The Dedekind’s Problem asks the number of monotone Boolean functions\, a(n)\, on n variables. Equivalently\, a(n) is the number of antichains in the n-dimensional Boolean lattice $[2]^n$. While the exact formula for the Dedekind number a(n) is still unknown\, its asymptotic formula has been well-studied. Since any subsets of a middle layer of the Boolean lattice is an antichain\, the logarithm of a(n) is trivially bounded below by the size of the middle layer. In the 1960’s\, Kleitman proved that this trivial lower bound is optimal in the logarithmic scale\, and the actual asymptotics was also proved by Korshunov in 1980’s. In this talk\, we will discuss recent developments on some variants of Dedekind’s Problem. Based on joint works with Matthew Jenssen\, Alex Malekshahian\, Michail Sarantis\, and Prasad Tetali.
URL:https://dimag.ibs.re.kr/event/2024-01-11/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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