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DTSTAMP:20201007T200000Z
UID:1601903941411@events.msu.edu
CATEGORIES:Conferences / Seminars / Lectures
DTSTART:20201007T200000Z
DTEND:20201007T210000Z
SUMMARY:Math Seminar Series
DESCRIPTION:
Seminar in Cluster algebras\n
\n
Bruce E. Sagan
will be speaking.\n
\n
The presentation is titled
"On a rank-unimodality conjecture of Morier-Genoud
and Ovsienko."\n
\n
This is a virtual
meeting that will be held over Zoom.\n
\n
The description
is as follows:\n
Let α=(a,b,...)
be a composition. Consider the associated
poset F(α), called a fence, whose covering
relations are x1⊲x2⊲...⊲xa+1⊳xa+2⊳...⊳xa+b+1⊲xa+b+2⊲...
.\n
We study the associated distributive
lattice L(α) consisting of all
lower order ideals of F(α). These lattices
are important in the theory of cluster
algebras and their rank generating functions
can be used to define q-analogues of rational
numbers. In particular, we make progress on
a recent conjecture of Morier-Genoud and Ovsienko
that L(α) is rank unimodal. We show
that if one of the parts of α is greater
than the sum of the others, then the conjecture
is true. We conjecture that L(α) enjoys
the stronger properties of having a nested
chain decomposition and having a rank sequence
which is either top or bottom interlacing,
the latter being a recently defined property
of sequences. We verify that these properties
hold for compositions with at most three
parts and for what we call d-divided posets,
generalizing work of Claussen and simplifying
a construction of Gansner.\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:Zoom link provided on Math Seminars page
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