Title: Type B q-Stirling numbers
| Speaker: | Joshua Swanson |
| Affiliation: | USC |
| Location: | MC 6029 or contact Logan Crew for Zoom link |
Abstract:
The
Stirling
numbers
of
the
first
and
second
kind
are
classical
objects
in
enumerative
combinatorics
which
count
the
number
of
permutations
or
set
partitions
with
a
given
number
of
blocks
or
cycles,
respectively.
Carlitz
and
Gould
introduced
q-analogues
of
the
Stirling
numbers
of
the
first
and
second
kinds,
which
have
been
further
studied
by
many
authors
including
Gessel,
Garsia,
Remmel,
Wilson,
and
others,
particularly
in
relation
to
certain
statistics
on
ordered
set
partitions.
Separately,
type
B
analogues
of
the
Stirling
numbers
of
the
first
and
second
kind
arise
from
the
study
of
the
intersection
lattice
of
the
type
B
hyperplane
arrangement.
We
combine
the
two
directions
and
introduce
new
type
B
q-analogues
of
the
Stirling
numbers
of
the
first
and
second
kinds.
We
will
discuss
connections
between
these
new
q-analogues
and
generating
functions
identities,
inversion
and
major
index-style
statistics
on
type
B
set
partitions,
and
aspects
of
super
coinvariant
algebras
which
provided
the
original
motivation
for
the
definition.
This
is
joint
work
with
Bruce
Sagan.
This
is
joint
work
with
physicists
Jean
Philippe
Labbe,
Julia
Liebert,
Eva
Philippe,
Arnau
Padrol,
and
Christian
Schilling.