Just my personal website
How many ways are there to distribute n n n undistinguishable items into k k k bins? Consider the following illustration for the situation where we distribute 7 7 7 items (stars) into 4 bins (intervals between bars) indicated by separators: ⋆ ⋆ | ⋆ ⋆ | | ⋆ ⋆ ⋆ \star~\star~\text{\textbar}~\star~\star~\text{\textbar}~\text{\textbar}~\star~\star~~\star ⋆ ⋆ | ⋆ ⋆ | | ⋆ ⋆ ⋆ We see that the problem is…
As a regular and avid podcast listener, I was looking for a solution to synchronize my subscriptions and episode status across several devices. On mobile, I use the excellent Antenna Pod app, while on desktop I rely on gPodder . Since the open-source synchronization server gPodder.net frequently encounters status 500 errors, I decided to set up my own synchronization server using the lightweight,…
Overview & Background Continuing the theme of last post , we will look at a classic result in graph theory, namely Dirac’s theorem on Hamiltonian cycles. This result was first published by Gabriel A. Dirac in 1952 [1] , with later refinements by Ore, as well as Bondy and Chvátal. Three proofs of the theorem will be presented: the original proof from Dirac’s paper, an induction proof, and a short…
Overview We will show that for a locally dense graph we can give a strong upper bound on the number of independent sets of a certain size. This specific method for graphs is an instance of the so-called container method , that allows to give bounds on structures appearing in larger objects with specific local properties. More specifically as applied to graph theory, this turns out to be quite…
Part 1 of this series went through the basic setup and customization of this blog for your own purposes. In this part, I will go through a few technical details, tips and additional notes, that can allow you to extend the site and troubleshoot errors. This part can also serve as a project reference or documentation of some sort. Overview Before we go into detail about different aspects of the…
In my Hello Internet post I announced my intention to write a post on how I set up this blog and how you can do the same. The time has now finally come, and the original idea has morphed into a two-part series. Enjoy! INFO This tutorial is primarily meant for beginners. It explains cloning this blog from Github, personalizing it with custom icons, name and color, and finally publishing it with…
You’ve probably already heard of the Fibonacci sequence. It is a sequence of numbers named after the mathematician Leonardo of Pisa , that’s generated using a simple rule, yet pops up in many unexpected places in math and nature, often in relation to the golden ratio. To generate the sequence, start with the sequence 1, 1 . Then, generate the next element in the sequence by adding up the last two…
Hi! This is the first post on my new blog, and I’m really excited. I hope to write more in the coming weeks and months, especially about technical and software-related topics. My goal is to write about current software side projects and things I’ve learned, all in the spirit of “Stay curious, keep learning”. Depending on how that works out, I’ll adapt if needed. Outlook A few topics I’d like to…