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                        Bar-Ilan Combinatorics Seminar
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The next meeting will be, IYH, on Sunday, 18 Iyar (May 22) at 16:00 pm
in Room 201 (Math Dept Seminar Room), Math and CS Building
 
Speaker: Arkadius Kalka (BIU)
 
Title: On the diameter of the Tits graph of the longest element
        in Coxeter groups of classical type
 
Abstract: Consider the Tits graph of the longest element of a finite
type Coxeter group. Its vertices are reduced words representing the
longest element, and edges correspond to one application of a
relation. By counting appropriate inversions Reiner and Roichman
([RR09], see:  <http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.4768v2.pdf)>
computed lower bounds for the diameter of this Tits graph for all
finite type Coxeter groups. Using methods from the theory of
hyperplane arrangements they proved for the families of A and B-type
that these lower bounds are exact. We give elementary proofs for the A
and B-type by showing that the Tits posets (poset structure given by
inclusion of these inversions) have unique maximal and minimal
elements. For the D-type Coxeter group, we show for several
``natural'' candidate bottom words that there exist other local
minimal elements in the Tits poset.
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Yuval Roichman   <yuvalr@macs.biu.ac.il>