Title: Non-crossing partitions
| Speaker: | Bruce Richmond |
| Affiliation: | University of Waterloo |
| Room: | MC 5501 |
Abstract:
It
is
well
known
that
a
partition,
$\pi$,
of
an
n-element
set
S
=
1,2,...,
n
is
a
set
of
disjoint
subsets,
called
blocks,
such
that
the
union
of
the
blocks
equals
S.
If
in
addition
the
blocks
of
$\pi$
have
the
property
that
if
$V_{i}$
and
$V_{j}$
are
any
two
blocks
of
$\pi$
then
it
is
not
possible
to
have
a
<
b
<
c
<
d
where
$a,
c
\in
V_{i}$
and
$b,d
\in
V_{j}$
then
$\pi$
is
called
non-crossing.
It
is
surprising
to
me
that
non-crossing
partitions
arise
in
several
seemingly
unrelated
contexts,
geometric
group
theory
(braid
groups),
free
probability,
matroid
theory
and
as
pointed
out
by
W.
T.
Tutte
also
in
the
Birkhoff-Lewis
equations
arising
in
map-colouring.
Most
of
the
talk
will
present
facts
following
Boyu
Li's
Masters
thesis.
The
last
part
of
the
talk
will
sketch
joint
work
with
B.
Li
and
A.
Nica.
It
will
describe
functional
equations
which
define
generating
functions
for
NC-partitions
with
various
restrictions
on
the
blocks.
This
allows
one
to
determine
the
distributions
defined
by
these
families
of
NC-partitions.