Friday, September 12, 2014 3:30 pm
-
3:30 pm
EDT (GMT -04:00)
Exponentially Dense Matroids
| Speaker: | Peter Nelson |
|---|---|
| Affiliation: | University of Waterloo |
| Room: | Mathematics 3 (M3) 3103 |
Abstract:
The
growth
rate
function
for
a
minor-closed
class
of
matroids
is
the
function
$h(n)$
whose
value
at
an
integer
n
is
the
maximum
number
of
elements
in
a
simple
matroid
in
the
class
of
rank
at
most
$n$;
this
can
be
seen
as
a
measure
of
the
density
of
the
matroids
in
the
class.
A
theorem
of
Geelen,
Kabell,
Kung
and
Whittle
implies
that
$h(n)$,
where
finite,
grows
either
linearly,
quadratically,
or
exponentially
with
base
equal
to
some
prime
power
$q$,
in
$n$.
I
will
discuss
growth
rate
functions
for
classes
of
the
exponential
sort,
determining
the
growth
rate
function
almost
exactly
for
various
interesting
classes
and
giving
a
theorem
that
essentially
characterizes
all
such
functions.