Cassie Naymie, Pure Mathematics, University of Waterloo
"Lev's bounds for subsets containing no 3-APs (Part 2)"
We
say
that
$\{x,y,z\}$
forms
a
three
term
arithmetic
progression
(or
3-AP)
if
$x+z=2y$.
For
a
finite
abelian
group
$G$
we're
interested
in
finding
the
largest
cardinality
of
all
subsets
$A\subseteq
G$
with
$A$
containing
no
3-APs.
We
denote
this
cardinality
by
$D(G)$.
In
this
talk
we
will
prove
a
result
of
Lev's
showing
how
$D(G)$
can
be
bounded
above
based
on
the
structure
of
the
group
$G$.