Title: Hopf algebras, colorings and simplicial complexes
Speaker: | Carolina Benedetti |
Affiliation: | York University |
Room: | MC 6486 |
Abstract:
Inspired
by
the
theory
pioneered
by
Stanley's
chromatic
symmetric
function
and
its
connection
to
Hopf
algebras,
we
will
see
how
abstract
simplicial
complexes
can
be
endowed
naturally
with
a
combinatorial
Hopf
structure
that
gives
rise
to
chromatic
generating
functions.
Using
principal
specializations
on
these
generating
functions
we
obtain
certain
combinatorial
identities
involving
acyclic
orientations
related
to
the
complexes.
We
will
explore
different
expansions
in
terms
of
symmetric
functions
of
these
chromatic
functions
and
derive
certain
information
of
the
complex
out
of
it.
If
time
permits,
we
will
discuss
work
in
progress
aiming
to
derive
the
analogous
of
Shareshian-Wachs
"chromatic
quasisymmetric
functions"
for
simplicial
complexes.
This
is
joint
work
with
Josh
Hallam
and
John
Machack.