A Lattice Path Combinatorial Approach to Rothe Numbers and Related Convolution Results

Issue title: Lattice Path Combinatorics and Applications

Article type: Research Article

Authors: Panny, Wolfgang

Affiliations: Applied Computer Science, Department of Information Systems and Operations, Vienna University of Economics and Business, Austria, [email protected]

Note: [] Address for correspondence: Applied Computer Science, Department of Information Systems and Operations, Vienna University of Economics and Business, Austria

Abstract: Rothe numbers (aka generalized Catalan numbers) have a natural interpretation in terms of lattice paths. Making use of this interpretation this paper aims at showing how some classical convolution identities involving Rothe numbers can also be proved conveniently using lattice path combinatorics.

Keywords: Lattice paths, Rothe numbers, generalized Catalan numbers, Rothe's identity, Hagen-Rothe formula

DOI: 10.3233/FI-2012-700

Journal: Fundamenta Informaticae, vol. 117, no. 1-4, pp. 265-277, 2012