Sophie Maclean Counting Polyominoes and Janet Axelrud Making New Math
It's really hard to know you've done these counting problems right, as I recall. There's a useful thing called called the Orbit-Stabilizer Theorem of a group action , but it's still easy to make a mistake. I guess that in these we're only talking about polyominoes made of squares, not ones made of equilateral triangles or hexagons, so it's not that complicated. Subscribe to Numberphile . Daniel Tubbenhauer has done a series of lectures on the Analytic Theory of Monoidal Categories, which is something he made up himself, I think. It's about the curious fact that some of these asymptotic formulae are far easier to prove than you might expect, based on how hard the underlying counting problems are. This is lecture one, which is actually the only part I even vaguely understand! The other four parts are in this playlist . Part II where he talks about sums and products and dimensions, ... I got lost about half-way through this one: Subscribe to Visual Math . Math...