Séminaire Lotharingien de Combinatoire, 80B.31 (2018), 12 pp.

Nickolas Hein and Jia Huang

Variations of the Catalan Numbers From Some Nonassociative Binary Operations

Abstract. We investigate certain nonassociative binary operations that satisfy a four-parameter generalization of the associative law. From this we obtain variations of the ubiquitous Catalan numbers and connections to many interesting combinatorial objects such as binary trees, plane trees, lattice paths, and permutations.

Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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