So I guess that this is my #introduction

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

#introduction 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...

URL: http://gosper.org/homeplate.html

Entry: https://read.somethingorotherwhatever.com/entry/OfficiallyHomePlateDoesntExist

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.

This stuff never ceases to amaze me - Haruki Nakamara's mechanical paper animals: https://geecr.com/product/nakamura-paper-toys

If you'll have more of these, maybe define some node styles? See e.g. hw8 at https://github.com/bmreiniger/academicSite/tree/2c66079a7188499e0623f1218e9649efab491d96/teaching/18Spring/hw

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?

While the baby is sleeping, I'm having fun working through the Lean natural numbers game https://wwwf.imperial.ac.uk/~buzzard/xena/natural_number_game/ #math

Donald Trump tests positive for COVID-19, and there's a huge spike in Google searches for 'schadenfreude' : https://trends.google.com/trends/explore?date=now%207-d&geo=US&q=schadenfreude

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?".

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! https://youtu.be/9T3zCsyx98g

Origametry: Mathematical Methods in Paper Folding (https://www.cambridge.org/us/academic/subjects/mathematics/recreational-mathematics/origametry-mathematical-methods-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 (https://books.google.com/books?id=LdX7DwAAQBAJ), but it looks interesting and worth waiting for.

- website
- https://bmreiniger.github.io

Combinatorist (esp. graph theorist) turned Data Scientist

Joined Jun 2017