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X-WR-CALDESC:Events for Discrete Mathematics Group
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BEGIN:VEVENT
DTSTART;VALUE=DATE:20250203
DTEND;VALUE=DATE:20250206
DTSTAMP:20260417T083334
CREATED:20250121T050727Z
LAST-MODIFIED:20250121T050727Z
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SUMMARY:IBS-DIMAG Winter School on Graph Minors\, Week 1
DESCRIPTION:
URL:https://dimag.ibs.re.kr/event/graph-minors-week-1/
LOCATION:Room B109\, IBS (기초과학연구원)
CATEGORIES:Workshops and Conferences
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250204T163000
DTEND;TZID=Asia/Seoul:20250204T173000
DTSTAMP:20260417T083334
CREATED:20241226T073135Z
LAST-MODIFIED:20241230T024913Z
UID:10324-1738686600-1738690200@dimag.ibs.re.kr
SUMMARY:Jang Soo Kim (김장수)\, Longest elements in a semigroup of functions and Slater indices
DESCRIPTION:The group \( S_n \) of permutations on \([n]=\{1\,2\,\dots\,n\} \) is generated by simple transpositions \( s_i = (i\,i+1) \). The length \( \ell(\pi) \) of a permutation \( \pi \) is defined to be the minimum number of generators whose product is \( \pi \). It is well-known that the longest element in \( S_n \) has length \( n(n-1)/2 \). Let \( F_n \) be the semigroup of functions \( f:[n]\to[n] \)\, which are generated by the simple transpositions \( s_i \) and the function \( t:[n]\to[n] \) given by \( t(1) =t(2) = 1 \) and \( t(i) = i \) for \( i\ge3 \). The length \( \ell(f) \) of a function \( f\in F_n \) is defined to be the minimum number of these generators whose product is \( f \). In this talk\, we study the length of longest elements in \( F_n \). We also find a connection with the Slater index of a tournament of the\ncomplete graph \( K_n \). This is joint work with Yasuhide Numata.
URL:https://dimag.ibs.re.kr/event/2025-02-04/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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