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The run transform

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2012Embargo end date: 01 Jan 2011 English Publisher:Elsevier BVJournal:Discrete Mathematics, volume 312, pages 2,927-2,937 (issn: 0012-365X,

Authors: Emeric Deutsch; David Callan;

doi: 10.1016/j.disc.2012.05.009 , 10.48550/arxiv.1112.3639

arXiv: http://arxiv.org/abs/1112.3639

The run transform

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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.

18 pages

Related Organizations

University of Chicago
United States
University of Wisconsin–Oshkosh
United States
University of Wisconsin–Madison
United States

Keywords

Noncrossing partition, Increasing run, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Dyck path, Combinatorics (math.CO), Pyramid ascent, 05A15, Theoretical Computer Science

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