The uplift principle for ordered trees

Gi-Sang Cheon,Louis Shapiro

doi:10.1016/j.aml.2011.11.018

Gi-Sang Cheon, Louis Shapiro

Open Access

https://doi.org/10.1016/j.aml.2011.11.018

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Journal: Applied mathematics letters	Publication Date: Nov 28, 2011
Citations: 8	License type: elsevier-specific: oa user license

Affiliation: Sungkyunkwan University, Howard University

Abstract

In this paper, we describe the uplift principle for ordered trees which lets us solve a variety of combinatorial problems in two simple steps. The first step is to find the appropriate generating function at the root of the tree, the second is to lift the result to an arbitrary vertex by multiplying by the leaf generating function. This paper, though self contained, is a companion piece to Cheon and Shapiro (2008) [2] though with many more possible applications. It also may be viewed as an invitation, via the symbolic method, to the authoritative 800 page book of Flajolet and Sedgewick (2009) [8] . Our examples, with one exception, are different from those in this excellent reference.

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