Polygon Dissections and Marked Dyck Paths
Arthur Cayley proved in 1890 that the number of ways to dissect a regular n-gon using i
noncrossing diagonals is
\frac{1}{i+1}\binom{n-3}{i}\binom{n+i-1}{i}. The purpose of this note is to point out that once the
problem is recast in terms of marked lattice paths, a simple
combinatorial method of counting Dyck paths applies almost verbatim
to obtain Cayley's result.
