Published on: 2025-05-08 07:29:29
Analytic Combinatorics -- A Worked Example 08 Apr 2025 - Tags: sage 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 analyt
Keywords: frac ldots left omega right
Find related items on AmazonPublished on: 2025-05-10 19:34:02
Formula 1 held the third round of its 2025 season at Suzuka in Japan yesterday. The race used to be held toward the end of the calendar, but F1 now visits while the cherry blossoms are blooming, which certainly makes for some good visuals. With a hefty timezone difference between Suzuka and fans in Europe and the US, a difficult decision must be made: Do I stay up all night to watch it live? Let's just say I was glad I did that for qualifying on Friday night—and I was equally glad I slept in the
Keywords: corner left like race suzuka
Find related items on AmazonPublished on: 2025-05-15 15:00:58
The Nintendo Switch 2 could be considered the most direct "sequel" to a Nintendo console that the company has ever made. The lineage is right there in the name, with Nintendo simply appending the number "2" onto the name of its incredibly successful previous console for the first time in its history. Nintendo's previous consoles have all differed from their predecessors in novel ways that were reflected in somewhat new naming conventions. The Switch 2's name, on the other hand, suggests that it
Keywords: joy left original right switch
Find related items on AmazonPublished on: 2025-06-03 02:23:34
One country, one cuisine. It’s a model of food that really underpins how people tend to think about, organize, and categorize food. Search Google Maps, and your local eateries are bound to be arranged into “Thai” or “Italian”. Hop over to Taste Atlas, and you’ll find little country flags next to each article. On Reddit’s /r/cooking, it’s practically a semi-annual tradition to see someone attempting to make ‘food around the world’, dutifully hopping around the globe nation-state by nation-state.
Keywords: dish left rice right soup
Find related items on AmazonPublished on: 2025-06-14 04:32:53
Robert Vanderbei has written a beautiful series of articles and talks about a method for finding the radius of the earth based on a single photograph of a sunset over a large, calm lake. Vanderbei’s analysis is an elegant and subtle exercise in classical trigonometry. In this post, I would like to present an alternative analysis in a different language: Geometric Algebra. I believe that geometric algebra is a more powerful system for formulating and solving trigonometry problems than the classi
Keywords: algebra geometric left product vectors
Find related items on AmazonPublished on: 2025-06-14 16:47:12
Kerning, the Hard Way 2025-03-14 by David Jones Here is a font i am working on; i hope you like it. The letterforms are reversed out against a vertically striped background. In a manner similar to Schaeffer Versalien. The graphic effect is inspired-by/stolen-from Schaefer Versalien, but the letterforms are modified from my found stencil font Arugula. Bear in the mind that with a font like this, the parts that are drawn are the black parts. So, let's consider a word like SALTY: Looks okay?
Keywords: font kerning left like right
Find related items on AmazonPublished on: 2025-06-21 05:47:43
Building on my previous post on sorting algorithms, I implemented the same algorithms using CUDA to explore performance improvements through parallel computing. The goal is to see how we can leverage the power of parallel computing to speed up our sorting algorithms. I went for a NVIDIA recruiting event some days ago, that was a great event and it motivated me to try to rewrite the sorting algorithms using CUDA. I’ll take merge sort as our test algorithm because it nicely divides the problem in
Keywords: array left long merge size
Find related items on AmazonPublished on: 2025-06-23 06:50:02
With co-author Brett Simmers! The Cinder JIT compiler does some cool stuff with how they represent types so I’m going to share it with you here. The core of it is thinking about types as sets (lattices, even), and picking a compact representation. Compilers will create and manipulate types with abandon, so all operations have to be fast. We’ll start from first principles, assuming we’re analyzing a language like Python, and build our way up to roughly what Cinder has (and we could go further f
Keywords: int left list struct type
Find related items on AmazonPublished on: 2025-06-25 19:01:35
Swipe from left to right for more comic collections.
Keywords: collections comic left right swipe
Find related items on AmazonPublished on: 2025-07-13 04:25:51
February 22, 2025 at 14:53 Tags Math There's a cute math puzzle that can be interesting to folks on very different levels: Given exactly four instances of the digit 2 and some target natural number, use any mathematical operations to generate the target number with these 2s, using no other digits. Some examples can be done by elementary school kids: \[\begin{align*} 1&=\frac{2+2}{2+2}\\ 2&=\frac{2}{2}+\frac{2}{2}\\ 3&=2\cdot2-\frac{2}{2}\\ 4&=2+2+2-2\\ 5&=2\cdot 2 +\frac{2}{2}\\ 6&=2\cdot 2\
Keywords: align frac left log_ sqrt
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