https://orcid.org/0000-0001-8270-2898
Summary
The Catalan numbers are the solution to hundreds of interesting counting problems. We consider a set of permutations counted not by the Catalan numbers, but by the squares of the Catalan numbers. While their enumeration is already known by more technical methods, we present a new proof by giving a bijection with pairs of arrangements of parentheses.
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Notes on contributors
Lara Pudwell
LARA PUDWELL (MR Author ID: 716641; Orcid ID: 0000-0001-8270-2898) is a Professor of Mathematics and Statistics at Valparaiso University and is the Executive Director of MathPath, a national residential summer camp for middle schoolers who love mathematics. This article was inspired by questions that arose in the Counting Permutations breakout class at MathPath 2022.