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 ...

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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 ...

In week241 of This Week’s Finds, you can follow me on my tour of the Laser Interferometry Gravitational-Wave Observatory in Louisiana: Also hear some tales of the dodecahedron… from the pyritohedron ...

This week in our seminar on Cohomology and Computation we continued discussing the bar construction, and drew some pictures of a classic example ...

John Baez has been struggling to understand the pi calculus — a formalism for modelling concurrency in computer science. I’m going to try to explain it nice and slowly. I’ll use the “polyadic ...

A while back Gina asked why computer scientists should be interested in categories. Maybe you categorical computer scientists out there have your own favorite answers to this? I’d be glad to hear them ...

Category Theory and Biology Posted by David Corfield Some of us at the Centre for Reasoning here in Kent are thinking about joining forces with a bioinformatics group. Over the years I’ve caught ...

Re: Integral Octonions (Part 12) Re: Puzzle 2, I have been told that there are nice constructions of quantum groups (nice meaning, in particular, not just by writing down generators and relations) ...

We should probably focus on the mathematicians who aren’t already blogging and perhaps don’t know much about it — since the ones who do, don’t need to read the Notices to learn about the issues. What ...

I think I’m gradually coming to understand why some people think (∞, 1) -toposes are the best thing since sliced bread. For me, I think a brief way to describe what’s so amazing about them is that ...

In Chris J . Isham A New Approach to Quantising Space-Time: I. Quantising on a General Category gr-qc/0303060 the author considers the concept of an arrow field on a category. I recall his definition, ...