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DTSTAMP:20200909T201000Z
UID:1599055475206@events.msu.edu
CATEGORIES:Conferences / Seminars / Lectures
DTSTART:20200909T201000Z
DTEND:20200909T210000Z
SUMMARY:Math Seminar Series
DESCRIPTION:
 Sheila Sundaram will be speaking. The presentation 
 is titles "On the homology of subword order." 
 \n
 \n
 The Zoom link can be found on the seminar 
 page linked below.\n
 \n
 In this talk we 
 examine the homology representation of the symmetric 
 group Sn on rank-selected subposets of 
 subword order. We show that the action on the 
 rank-selected chains is a nonnegative integer 
 combination of tensor powers of the reflection 
 representation S(n−1,1) indexed by 
 the partition (n−1,1), and that its Frobenius 
 characteristic is h-positive and supported 
 on the set T1(n)={hλ:λ=(n−r,1r),r≥1}. 
 We give an explicit formula 
 for the homology module for words of bounded 
 length, as a sum of tensor powers of S(n−1,1). 
 This recovers, as a special case, 
 a theorem of Bj"orner and Stanley for words 
 of length at most k. We exhibit a curious duality 
 in homology in the case when one rank is 
 deleted. We also show that in many cases, the 
 rank-selected homology modules, modulo one 
 copy of the reflection representation, are h-positive 
 and supported on the set T2(n)={hλ:λ=(n−r,1r),r≥2}. 
 Our analysis 
 of the homology also uncovers curious 
 enumerative formulas that may be interesting 
 to investigate combinatorially.\n\n
 Price: free\n
 Sponsor: Department of Mathematics\n
 Sponsor's Homepage: https://www.math.msu.edu/\n
 Contact name: Department of Mathematics\n
 Contact phone: (517) 353-0844\n
 for more info visit the web at:\n 
 https://www.math.msu.edu/Seminars/CalendarView.aspx?month-of=September2016\n
LOCATION:Online via Zoom
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