Generalized Catalan Numbers from Hypergraphs

Authors

Paul E. Gunnells, University of Massachusetts Amherst

Publication Date

2021

Journal or Book Title

Electronic Journal of Combinatorics

Abstract

The Catalan numbers C_n ∈ {1,1,2,5,14,42,…} form one of the most venerable sequences in combinatorics. They have many combinatorial interpretations, from counting bracketings of products in non-associative algebra to counting plane trees and noncrossing set partitions. They also arise in the GUE matrix model as the leading coefficient of certain polynomials, a connection closely related to the plane trees and noncrossing set partitions interpretations. In this paper we defi ne a generalization of the Catalan numbers. In fact we defi ne an infinite collection of generalizations C_n^(m) , m >= 1, with m = 1 giving the usual Catalans C_n; the sequence C_n^(m) comes from studying certain matrix models attached to hypergraphs. We also give some combinatorial interpretations of these numbers.

ISSN

1077-8926

DOI

https://doi.org/10.37236/8733

Volume

28

Issue

1

License

UMass Amherst Open Access Policy

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Funder

NSFNational Science Foundation (NSF) [DMS 1501832]

Recommended Citation

Gunnells, Paul E., "Generalized Catalan Numbers from Hypergraphs" (2021). Electronic Journal of Combinatorics. 1321.
https://doi.org/10.37236/8733