How do you count rooted planar n -ary trees with some number of leaves? For n = 2 this puzzle leads to the Catalan numbers. These are so fascinating that the combinatorist Richard Stanley wrote a ...

How to Count n-Ary Trees How do you count rooted planar n-ary trees with a given number of leaves? Use Lagrange inversion! TeXnical Issues Sage advice on viewing this blog and posting comments thereon ...

Last time I began explaining how a chunk of combinatorics is categorified ring theory. Every structure you can put on finite sets is a species, and the category of species is the free symmetric 2-rig ...

Here’s my second set of lecture notes for a 4 1 2 \frac{1}{2}-hour minicourse at the Summer School on Algebra at the Zografou campus of the National Technical University of Athens. Part 1 is here, and ...

Species and their generating functions Combinatorics, or at least part of it, is the art of counting. For example: how many derangements does a set with n n elements have? A derangement is a bijection ...