So I guess that this is my

I am a PhD student in Glasgow, in the university of Strathclyde, mostly studying category theory and monoidal category adjacent things. Right now, I am really into Hopf Monads

I completed my paper about the optimal size of 11 and 12-channel sorting networks.
It contains new theory, a search procedure, implementation details and formal verification of the result.

I'm now looking for some feedback before I make it public. DM me if you are interested 1/3

Hello mathstodon! I'm a PhD student in Canada, and I am originally from the UK. I'm researching topics related to higher category theory and homotopy type theory, but I generally am interested in foundations of mathematics, topology and algebra.

I was getting tired of the barrage of adverts on Twitter and this seems like a nice alternative. Also, I like that we can use \(\LaTeX\) here.

What I want to know is: what mathematical objects have you been thinking about recently?

Officially, Home Plate doesn’t exist.
Web page by Bill Gosper
In collections: Easily explained, Geometry
The official Major League and Little League rule books require the two “slanty” sides to be 12” long and meet at a right angle at the rear corner toward the catcher. This is where the foul lines meet. The left and right sides of Home Plate must poke into fair territory by half the width of the plate, which is 8½” (17” divided...
Entry: read.somethingorotherwhatever.

streaming, uspol, birdsite 

Can't wait for Alexandria Ocasio-Cortez's stream today.

It's well known that you can find eight 7-bit binary words all at Hamming distance 4 from one another (and 8 is maximal). What I never noticed before is that, if you start building such a list heedlessly, adding one new word at a time checking only that it's distance 4 from all the words already chosen, you CANNOT LOSE. You'll never get stuck; you'll always make it to eight. I have to think about that some more until it no longer seems to be a surprising and joyous geometrical conspiracy.

If you'll have more of these, maybe define some node styles? See e.g. hw8 at
The common node style gets defined in the `graph` environment in the preamble. You should be able to use `right of` instead of my manual label placement, and probably there's a way to generate the node with an offset label more directly?

Rose is red, violets blue,
Sugar's sweet and so are you,
Then add another bit,
Wait this ain't a lymrick,
My poem! What the fuck did you do!?!?

Donald Trump tests positive for COVID-19, and there's a huge spike in Google searches for 'schadenfreude' :

- A regular polyhedron has equal edges and equal vertex angles

*holds up infinite square tiling*
- Behold, a regular polyhedron

To be clear, I agree with the other thread here, that the other definitions are more natural. I'm approaching this from "how can we show this directly?".

@ColinTheMathmo (cc @tpfto)
Trickier, sure, but I think my vague approach above works. Lemme try to describe some more (maybe a proofinatoot later); it's similar to the classic exercise that shows that the power of prime \(p\) in \(k!\) is \(\sum_{i\geq1} \left\lfloor\frac k{p^i}\right\rfloor\) \) (which I now realize has a name, "Legendre's formula"). The idea extends to say that the power of prime \(p\) in the falling factorial \(n^{\underline{k}}\) is _at least_ that quantity.

Cancel the (n-k)!, and we're left with "why does k! divide the falling factorial \(n^{\underline{k}}\)?" (notation aside). And that can be answered, I think, with an understanding of divisibility by prime powers in ranges of consecutive integers.

The dLX (pronounced "d-Lex", as in "lexicon"), is a new 60-sided, alphabetical die from The Dice Lab. Sixty is enough for us to get a letter distribution that is close to the distribution in the English language, so they can be used for word search games!

@kimreece @hex
Is "kittens always go quantum in the end" the new "cats always land on their feet"?

Origametry: Mathematical Methods in Paper Folding (, new book coming out October 31 by @tomhull

I haven't seen anything more than the blurb linked here and the limited preview on Google Books (, but it looks interesting and worth waiting for.

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