Title: Minimal orbits of promotion
| Speaker: | Kevin Purbhoo |
| Affiliation: | University of Waterloo |
| Room: | MC 5501 |
Abstract:
Promotion
is
an
invertible
operation
on
linear
extensions
of
posets,but
most
of
the
motivation
for
studying
it
is
limited
to
a
few
special
families
of
posets.
For
"rectangle-shaped"
posets,
promotion
provides
a
combinatorial
model
for
a
variety
of
different
algebraic
phenomena.
Using
these
it
is
possible
to
determine
the
orbit
structure
of
the
promotion
map.
Unfortunately,
while
the
orbit
structure
is
completely
described
algebraically,
no
corresponding
combinatorial
bijection
is
known.
This
leads
to
a
strange
and
unsatisfying
state
of
affairs.
For
large
rectangles
it
is
trivial
to
count
orbits
of
a
given
size,
but
completely
impractical
produce
even
a
single
example.
The
problem
of
finding
an
explicit
bijection
appears
to
be
quite
hard
in
general.
I
will
talk
about
some
recent
progress:
the
case
of
minimal
orbits.
This
is
joint
work
with
David
Rhee.