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 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 ...

By the theorem, to put an F -structure on S is to partition S into nonempty parts, put an Exp -structure on the set of parts, and put an X 2 2! -structure on each part. But there’s just one way to put ...

Exercise 5. If you know about coproducts, you can show that F + G is the coproduct of F and G in the category of species, Set E, which we defined last time. Exercise 6. If you know about products, you ...

These are some lecture notes for a 4 1 2 \frac {1} {2} -hour minicourse I’m teaching at the Summer School on Algebra at the Zografou campus of the National Technical University of Athens. To save time ...