Friday, April 8, 2016 3:30 pm
-
3:30 pm
EDT (GMT -04:00)
Title: Permutation factorization and methods from mathematical physics
| Speaker: | Sean Carrell |
| Affiliation: | University of Waterloo |
| Room: | MC 5501 |
Abstract:
Given
a
full
cycle
$\pi$
in
the
permutation
group
on
$n$
points
one
may
ask
the
number
of
factorizations
of
$\pi$
into
a
minimal
number
of
transpositions,
in
this
case
$n-1$.
It
is
classically
known
that
the
number
of
such
factorizations
is
equal
to
$n^{n-2}$,
the
number
of
labelled
trees
on
$n$
vertices.
This
is
the
first
of
a
number
of
permutation
factorization
problems
of
interest
to
enumerative
combinatorialists,
some
of
which
have
connections
to
algebraic
geometry
and
mathematical
physics.
We
will
survey
a
number
of
these
permutation
factorization
problems
along
with
some
of
the
tools,
borrowed
from
physics,
used
to
study
them.