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DTSTART:20230101T000000
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DTSTART;TZID=Asia/Seoul:20240910T163000
DTEND;TZID=Asia/Seoul:20240910T173000
DTSTAMP:20260415T184257
CREATED:20240807T055137Z
LAST-MODIFIED:20240807T083739Z
UID:9690-1725985800-1725989400@dimag.ibs.re.kr
SUMMARY:Zhihan Jin (金之涵)\, The Helly number of Hamming balls and related problems
DESCRIPTION:We prove the following variant of Helly’s classical theorem for Hamming balls with a bounded radius. For $n > t$ and any (finite or infinite) set $X$\, if in a family of Hamming balls of radius $t$ in $X$\, every subfamily of at most $2^{t+1}$ balls have a common point\, so do all members of the family. This is tight for all $|X| > 1$ and all $n > t$. The proof of the main result is based on a novel variant of the so-called dimension argument\, which allows one to prove upper bounds that do not depend on the dimension of the ambient space. We also discuss several related questions and connections to problems and results in extremal finite set theory and graph theory. This is joint work with N. Alon and B. Sudakov.
URL:https://dimag.ibs.re.kr/event/2024-09-10/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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