is a collection of combinatorial objects.
=>
if there exist a sizepreserving bijection between
Q1
Prove that number of Dyck Paths
 Label all the points

if is an edge, , then we draw an edge 
Finish by drawing an
OGF
Q2
Find the value of
take
HW
Find the value of
Q4
Q5
Prove
m is an even number
Q6
Prove
HW
Prove
Thm
The OGF's for partitions
using parts in
partitions with largest part
all partitions,are
Def
a run is a maximal increasing string in the word
84135726 has 4 runs: 8, 4, 1357, 26
The Eulerian number
is the number of permutations of
Thm (Worpitzky's Identity)
: number of functions from
boxes, there can be nothing in a box, or some balls in a box. If there are some balls in a box, then list the balls from small to large, like:
separates,
so the answer is