Hacker News with Generative AI: Combinatorics

Analytic Combinatorics – A Worked Example (grossack.site)
Another day, another blog post that starts with “I was on mse the other day…”. This time, someone asked an interesting question amounting to “how many unordered rooted ternary trees with $n$ nodes are there, up to isomorphism?”. I’m a sucker for these kinds of combinatorial problems, and after finding a generating function solution I wanted to push myself to get an asymptotic approximation using Flajolet–Sedgewick style analytic combinatorics!
Graph Theory and Additive Combinatorics (yufeizhao.com)
Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics.
Mathematics of the daily word game Waffle (arxiv.org)
We investigate the combinatorics of permutations underlying the the daily word game Waffle, and learn why some games are easy to solve while extreme games are very hard. A perfect unscrambling must have precisely 11 orbits, with at least one of length 1, on the 21 squares.
Minimum bipartite matching via Riemann optimization (2023) (ocramz.github.io)
Some time ago I ran into two separate instances of the same combinatorial optimization problem in the span of a few days, and decided to read up a little on the fundamentals. The two applications were object tracking in videos, and peak alignment in chromatography data.