Séminaire Lotharingien de Combinatoire, 78B.39 (2017), 12 pp.

Nicolas Borie

Three-Dimensional Catalan Numbers and Product-Coproduct Prographs

Abstract. We present the new combinatorial class of product-coproduct prographs which are planar assemblies of two types of operators: products having two inputs and a single output and coproducts having a single input and two outputs. We show that such graphs are enumerated by the 3-dimensional Catalan numbers. We present some combinatorial bijections positioning product-coproduct prographs as key objects to probe families of objects enumerated by the 3-dimensional Catalan numbers.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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