The Run Transform
Combinatorics
2011-12-16 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1112.3639,
title = {The Run Transform},
author = {David Callan and Emeric Deutsch},
journal= {arXiv preprint arXiv:1112.3639},
year = {2011}
}
Comments
18 pages