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 ...

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 ...

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 ...