The Run Transform
We consider the transform from sequences to triangular arrays defined
in terms of generating functions by f(x) ->
(1-x)/(1-xy)*f((x(1-x))(1-xy)). We establish a
criterion for the transform of a nonnegative sequence to be
nonnegative, and we show the transform counts certain classes of lattice paths
by number of so-called pyramid ascents and certain classes of partitions into sets
of lists (blocks) by number of blocks that consist of increasing consecutive integers.
