Title: Solving
Prellberg
and
Mortimer's
conjecture
-
bijection(s)
between
Motzkin
paths
and
triangular
walks
| Speaker: | Julien Courtiel |
| Affiliation: | Université de Caen |
| Zoom: | Contact Karen Yeats |
Abstract:
In
these
difficult
times,
what
we
need
to
feel
better
is
some
colorful
and
elegant
bijections.
This
talk
introduces
the
work
we
did
with
Andrew
Elvey-Price
(Tours,
France)
and
Irène
Marcovici
(Nancy,
France).
Together
we
answered
an
open
question
from
Mortimer
and
Prellberg,
asking
for
a
bijection
between
a
family
of
walks
inside
a
bounded
triangular
domain
(think
about
a
large
equilateral
triangle
subdivided
in
several
smaller
equilateral
triangles)
and
the
famous
Motzkin
paths,
but
which
have
bounded
height.
The
used
techniques
for
the
proof
are
quite
elementary,
and
seem
to
be
robust.
Indeed,
in
addition
to
solving
Mortimer
and
Prellberg's
conjecture,
our
approach
enabled
us
to
find
a
new
surprising
bijection between
3D-walks
constrained
inside
a
pyramid
and
some
2D-walks
in
a
squared
grid.