Department of Mathematics
Moments and the Cut and Paste for Lattice Paths
Robert Sulanke
Boise State University
Abstract. Let U(2n) denote the
set of lattice paths that run from (0,0) to (2n,0) with the permitted
steps (1,1) and (1,-1). Let E(2n+2) denote the
set of paths in U(2n+2) that run strictly above the horizontal axis
except initially and finally.
Starting with Wallis' well-known formula for computing 
as
an infinite product, we first establish an interest
in lattice path configurations and their
moments. We then introduce
the cut and paste bijection
which relates points under paths of E(2n+2)
to points on paths of U(2n).
We apply this bijection
to obtain enumerations, some involving the Narayana distribution.
We also extend the bijection to a formula
relating factorial moments for the paths of E(2n+2) to moments
for the paths of U(2n).
All interested persons are welcome.
This talk will be accessible to M187 students.