Séminaire Lotharingien de Combinatoire, 78B.39 (2017), 12 pp.
Three-Dimensional Catalan Numbers and Product-Coproduct Prographs
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
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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