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CATALAN'S TRAPEZOIDS
Published online by Cambridge University Press: 18 March 2014
Abstract
Named after the French–Belgian mathematician Eugène Charles Catalan, Catalan's numbers arise in various combinatorial problems [12]. Catalan's triangle, a triangular array of numbers somewhat similar to Pascal's triangle, extends the combinatorial meaning of Catalan's numbers and generalizes them [1,5,11]. A need for a generalization of Catalan's triangle itself arose while conducting a probabilistic analysis of the Asymmetric Simple Inclusion Process (ASIP) — a model for a tandem array of queues with unlimited batch service [7–10]. In this paper, we introduce Catalan's trapezoids, a countable set of trapezoids whose first element is Catalan's triangle. An iterative scheme for the construction of these trapezoids is presented, and a closed-form formula for the calculation of their entries is derived. We further discuss the combinatorial interpretations and applications of Catalan's trapezoids.
- Type
- Research Article
- Information
- Probability in the Engineering and Informational Sciences , Volume 28 , Issue 3 , July 2014 , pp. 353 - 361
- Copyright
- Copyright © Cambridge University Press 2014
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