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 ...

Following SoTFom II, which managed to feature three talks on Homotopy Type Theory, there is now a call for papers announced for SoTFoM III and The Hyperuniverse Programme, to be held in Vienna, ...

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 ...

The Riemann Hypothesis claims that all the zeros of the zeta function lie on this line, except for the so-called trivial zeros at 2, 4, 6, 8 and so on. Riemann only checked this for the first three ...

Why Mathematics is Boring I don’t really think mathematics is boring. I hope you don’t either. But I can’t count the number of times I’ve launched into reading a math paper, dewy-eyed and eager to ...

for each object X, Y, Z in 𝒞. These are subject to the following conditions. The simplex category Δ and its subcategory Δ ⊥ A simple example of a skew monoidal category, that we will base the ...

These are some lecture notes for a 4 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, I am ...

In Haskell notation, the example reads as follows. matchAddress :: String -> Either Address Postal buildAddress :: Postal -> Address Traversals We can go further: optics do not necessarily need to ...

Yes, both sets of co-authors should be corrected. The pyknotic team is Clark Barwick and Peter Haine. The condensed team is Dustin Clausen and Peter Scholze. There’s some relation with the ...

The discussion on Tom’s recent post about ETCS, and the subsequent followup blog post of Francois, have convinced me that it’s time to write a new introductory blog post about type theory. So if ...

That is correct. There are finite index subgroups of profinite groups that are not open, i.e., there are profinite groups that do not equal their own profinite completion. However, by definition, the ...

On the one hand, an ultrafilter on a set can be seen as a primitive sort of probability measure, in which every subset is assigned a probability of either 0 or 1 and the measure only has to be ...