  Let $\pi$ be a set partition of $[n]=\{1,2,...,n\}$. The standard
representation of $\pi$ is the graph on the vertex set $[n]$ whose edges are
the pairs $(i,j)$ of integers with $i<j$ in the same block which does not
contain any integer between $i$ and $j$. The front representation of $\pi$ is
the graph on the vertex set $[n]$ whose edges are the pairs $(i,j)$ of integers
with $i<j$ in the same block whose smallest integer is $i$. Using the front
representation, we find a recurrence relation for the number of $12...
k12$-avoiding partitions for $k\geq2$. Similarly, we find a recurrence relation
for the number of $k$-distant noncrossing partitions for $k=2,3$. We also prove
that the front representation has several joint symmetric distributions for
crossings and nestings as the standard representation does.
