The Run Transform

Details The Run Transform The Run Transform

2011-12-15

arxiv.org/abs/1112.3639v1

Mathematics

Combinatorics

18 pages

Scientific paper

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 that the transform counts certain classes of lattice paths by number of "pyramid ascents", as well as certain classes of ordered partitions by number of blocks that consist of increasing consecutive integers.

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