Title: Circuit-hyperplane relaxation and matroid representation
| Speaker: | Jim Geelen |
| Affiliation: | University of Waterloo |
| Room: | MC 5501 |
Abstract:
Relaxing
a
circuit-hyperplane
in
a
representable
matroid
can
destroy
representability.
Indeed,
both
the
non-Pappus
matroid
and
the
V\’
amos
matroid
are
obtained
by
relaxing
a
circuit-hyperplane
in
a
representable
matroid.
We
characterize
the
GF(4)-representable
matroids
that
have
a
circuit-hyperplane
whose
relaxation
is
also
GF(4)-representable.
We
hope
to
use
the
same
techniques
for
GF(5)-representability,
which
will
hopefully
lead
to
the
excluded-minor
characterization
for
the
class
of
GF(5)-representable
matroids.
This
is
joint
work
with
Rutger
Campbell
and
Geoff
Whittle.
Parts
of
the
talk
will
require
some
understanding
of
matroid
theory,
but
our
main
question
can
be
stated
in
terms
of
matrices,
and
significant
parts
of
the
talk
will
be
accessible
to
people
who
have
no
prior
exposure
to
matroids.