Catalan Numbers Page

Content: Below is a list of articles on a diverse topics related to Catalan numbers and their generalizations. I emphasized historically significant works, as well as some bijective, geometric and probabilistic results.

Warning: This list is vastly incomplete as I included only downloadable articles and books (sometimes, by subscription) that I found useful at different times. I do plan to gradually expand it, but will try not to overwhelm the list, so many related results can be obtained by forward and backward reference searches. Let me know if you find it useful.


Larger values: at OEIS. Examples and Images: Catalan numbers (MacTutor History of Math.) Another meaning.

Encyclopedia and survey articles:

Catalan numbers history articles:

Introductory articles:

Videos of introductory lectures:

Videos of research lectures:

Historical articles:

Trees and other combinatorial interpretations:

Polygon dissections and noncrossing partitions:

Motzkin, Riordan and Baxter numbers:

Fine and Schröder numbers:

Lattice walks and generalized ballot numbers:

Pattern avoidance:

q-Catalan numbers:

q,t-Catalan numbers:

Hyperplane arrangements:

Generalization to Coxeter groups:

Catalan matroid:

Graph of triangulations:


Asymptotic and probabilistic results:

Random walks:


The images of road signs and binary trees used above are taken from Wikpedia.

The first two animated gifs of Dyck paths are takes from, the last one is made by Alejandro Morales (it circles over all 5 excited diagrams in a staircase shape).

We thank Xavier Viennot for giving scans of Euler's original letter, and most recently telling us about the Arbogast forgotten reference (Nov 2020).

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Last updated: 11/24/2020