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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."
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The Zoom link can be found on the seminar
page linked below.\n
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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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