Three-dimensional Catalan numbers and product-coproduct prographs

Nicolas Borie (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

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.

Mots clés: Catalan numbers; Prographs; Bijections; Young tableaux; Up-down permutations; Weighted Dyck paths

Domaines: Combinatoire [math.CO]

Nicolas Borie. Three-dimensional Catalan numbers and product-coproduct prographs. FPSAC 2017 The 29th international conference on Formal Power Series and Algebraic Combinatorics, Jul 2017, London, United Kingdom. ⟨hal-01743972⟩