The Fine numbers refined

Authors:
Gi-Sang Cheon;Sang-Gu Lee;Louis W. Shapiro
Affiliations:
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea;Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea;Department of Mathematics, Howard University, Washington, DC 20059, USA
Venue:
European Journal of Combinatorics
Year:
2010

Citing 5
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Abstract

We give a short combinatorial proof of a Fine number generating function identity and then explore some of the ramifications in terms of random walks, friendly walkers, and ordered trees. The results are also generalized to obtain similar results including those in Motzkin and Schroder settings.