Some instances of the cyclic sieving phenomenon on increasing tableaux
| Speaker: | Terry Visentin |
|---|---|
| Affiliation: | University of Winnipeg |
| Room: | Mathematics and Computer Building (MC) 5479 |
Abstract:
Let
X
be
a
finite
set,
<g>
a
cyclic
group
of
order
n
acting
on
X
and
f
a
polynomial
in
Z[q].
Then
a
triple
(X,<g>,f)
exhibits
the
cyclic
sieving
phenomenon
if
for
all
m,
the
number
of
elements
of
X
fixed
by
g^m
is
f(\omega^m)
where
\omega
is
an
nth
root
of
unity.
An
increasing
tableau
is
a
Young
tableau
where
the
entries
are
increasing
along
rows
and
columns.
Recently,
Pechenik
gave
an
instance
of
the
cycling
sieving
phenomenon
using
jeu
de
taquin
for
increasing
tableaux
of
rectangular
shape
with
two
rows.
In
this
talk,
we'll
discuss
this
result
and
an
instance
of
cyclic
sieving
on
increasing
tableaux
of
hook
shape.
Since
the
polynomial
f
is
usually
a
q-analoque
of
a
counting
formula
for
X,
we'll
begin
with
a
summary
of
some
enumerative
results
for
increasing
tableaux.
This
will
involve
looking
at
some
generalizations
of
Schr\"oder
paths.
(Joint
work
with
Tim
Pressey
and
Anna
Stokke.)