The Erdos-Ko-Rado Theorem, An Algebraic Perspective
Speaker: | Karen Meagher |
---|---|
Affiliation: | University of Regina |
Room: | Mike & Ophelia Lazaridis Quantum-Nano Centre (QNC) 0101 |
Abstract:
Several
years
ago
I
had
the
good
fortune
to
have
an
extremely
productive
post-doctoral
fellowship
with
Chris.
Our
work
from
this
period
has
culminated
in
a
book
about
the
Erdos-Ko-Rado
Theorem
(that
is
$\epsilon$
away
from
completion!)
This
theorem
is
a
major
result
in
extremal
set
theory.
It
gives
the
exact
size
and
structure
of
the
largest
system
of
sets,
with
a
fixed
number
of
elements,
that
has
the
property
that
any
two
sets
in
the
system
have
at
least
one
element
in
common.
There
are
many
extensions
of
this
theorem
to
combinatorial
objects
other
than
set
systems,
such
as
vectors
subspaces
over
a
finite
field,
integer
sequences,
partitions,
and
recently,
there
have
been
several
results
that
extend
the
EKR
theorem
to
permutations.
During
my
post-doc
with
Chris,
we
worked
on
an
algebraic
approach
to
proving
the
EKR
theorem
for
several
types
of
combinatorial
objects.
This
method
is
the
focus
of
our
book
and
will
be
the
focus
of
my
talk.
I
will
explain
this
method
by
showing
how
it
can
be
used
to
prove
that
the
natural
extension
of
the
EKR
theorem
holds
for
the
symmetric
group.