how many edges to guarantee ham-cycle?
[05-23-23]
A common question in extremal graph theory is "what conditions do I have to put on my graph to get property X" In this blog post, we investigate the question: how many edges to guarantee hamiltonian-cycle?
Binomial coefficients $\mod p$
[03-12-23]
Have you ever wondered what binomial coefficients look like $\mod p$? turns out there is actually a simple answer. Credit to Enumerative Combinatorics for the problem
robot panda gardener
[robot_panda_gardener]
I read a cool paper [Bilò, Davide, et al. “Cutting Bamboo Down to Size.” arXiv preprint arXiv:2005.00168 (2020)](https://arxiv.org/abs/2005.00168) and wrote a little "summary" of it. | very chill and very awesome!
prefix sum of binomial coefficients
[01-19-23]
Binomial coefficients come up all over the place in combinatorics. This article gives a decent bound on the sum of a prefix of binomial coefficients. The bound get's pretty tight for like $(.1n, .5n)$, but if you can find something tighter, please let me know!
KST theorem
[12-25-23]
I wanted to tell my sister about the KST theorem, so I'm writing it down here really fast first to make sure I understand it.
finding an n-gon
[08-03-23]
More than $1-\frac{1}{n}$ of the circumference of a circle is colored black. Can you draw a regular $n$-gon on the circle with all vertices in black regions?
subset sums
[02-21-24]
Jacob Foxs gave a nice talk about subset sums today. I summarize what I remember from it.
tribes
[02-15-24]
I explore a remark that was made today in Dor Minzer's class on analysis of boolean functions.
boolean analysis: hypercontractivity
[02-22-24]
This is a stub. I will *expand* it later. I'm serious pun aside. I really didn't have time to write it all down yet.
elevator: simple variants
[01-23-23]
Analysis of a couple of variants of a novel scheduling problem proposed by Nathan.
useful bounds
[10-01-23]
today I spent way too long searching for a bunch of common bounds that are useful in, e.g., randomized algorithm analysis. Here are the bounds I found, a gift to a future myself.
hales jewett
[02-28-23]
finding a monochromatic arithmetic progression in a coloring of some numbers. And playing tick tack toe in high dimensions.
2 agent auction
[10-09-23]
Selling and buying, how hard could it be? I'm not going to lie, it could be pretty simple.
max-anti-chain vs min-chain-cover
[04-06-23]
A hint of duality between chains and anti-chains in posets.
mono rectangle
[07-29-23]
In any finite coloring of $\Z^2$ there is a monochromatic axis aligned rectangle.
Probabilistic Method
[probabilistic_method]
I am going to try to read "The Probablistic Method" by Noga Alon and Joel H. Spencer. The Probablistic Method, pioneered by Erdos, is a really interesting way to think about combinatorics problems. Here is a high level overview of how proofs by the probabilistic method go
