Anyone hear of this before, or can find something about it? It seemed kinda cool at the time, and I like this axiomatization.
Background: A finite projective plane has point-line duality, and affine planes lack it. You can get a projective plane by adding a "line at infinity," and this is reversible.
Years ago I stumbled across this in constructing a counterexample to a graph conjecture, and I never found out if it was something people had realized or used before:
We can also recover point-line duality from an affine plane by just deleting one of the parallel classes of lines. <cont...>
#proofinatoot that if a finite poset has a unique maximal \(x\), then \(x\) is maximum.
If not, there is a \(y_1||x\). \(y_1\) is not maximal, so there is \(y_2>y_1\); we cannot have \(y_2<x\), else transitivity would give \(y_1<x\), and we cannot have \(y_2>x\) because \(x\) is maximal, so \(y_2||x\). Continuing, we build a chain \(y_1<y_2<\dotsb\) (with \(y_i||x\) for all \(i\)), contradicting finiteness.
(This proof also suggests a construction of an infinite poset without the property.)
If you are in the EU and have not yet heard of this vote. There is a European's citizens Initiative for a Universal Basic Income. This is an EU binding vote. https://eci.ec.europa.eu/014/public/#/screen/home . There is only 5 days left and over 700,000 votes still needed. Please vote.
Can anyone translate this page into English?
It seems to be an interview of Sính. Under this photo it says "Cót village girl is passionate about math".
based on the people i know who work in tech, when it comes to their home computers, 33 percent of the time it's a "cobbler's children have no shoes" situation, 33 percent a "cobbler's children have brand-new sneakers" situation, and rest, the lesser-known,"the cobbler's children wear mismatched shoes with rubber the cobbler started vulcanizing in their garage until they got bored" situation.
I was really depressed for the last two days because I left my ring on the lawn and the crows stole it BC shiny. It's irreplaceable and Akkas gave it to me two years ago so I was devastated. I dredged the pond and used a metal detector all over the lawn but it was gone. But today I cooked the crows bacon in the morning and this afternoon it was returned RIGHT WHERE I LEFT THE BACON!!!!!
You may have seen studies that test how experts evaluate verbal expressions of uncertainty, such as (very) likely, in terms of probability values. https://en.wikipedia.org/wiki/Words_of_estimative_probability
Image source: https://github.com/zonination/perceptions
One robust finding is that most probabilistic expressions may correspond with a wide range of probability values. 1/2
I bet someone here can settle it quickly: does Bernoulli's lemniscate
(x² + y²)² = x² - y²
define an elliptic curve when we work over the complex numbers? If so, is this elliptic curve isomorphic to the complex numbers modulo the Gaussian integers?
(6/n, n = 6)
New blog post: Maybe powers of \(\pi\) don't have unexpectedly good approximations?
(Walking back my suggestion from a recent post that they do, after some statistical tests failed to find anything unusual about how well they can be approximated.)
A while ago @davidphys1 asked why nobody had made animations of the shunting yard algorithm with cutesy trains.
There is no surer way to summon me!
I've spent some of my spare time over the bank holidays making exactly that: https://somethingorotherwhatever.com/shunting-yard-animation/
Here's a question that could be a high school mathematics project or something. A k-regular graph has the obvious property that the sum of the degrees of the neighbours of v is equal to k times the degree of v, for each vertex v. But what other graphs have this property? I don't think there's a general rule (maybe I'm wrong!) but start with k=1,2,3 for instance. Follow up questions: can you prove you've found them all? What about infinite graphs/multigraphs? etc.
From Neil Calkin on FFB:
"If this holds up --- and both of them are fabulous mathematicians, then it is huge. David Jackson announced just now that he and Bruce Richmond have a 5 page proof of the 4 color theorem.
"I hope that the proof is along the lines: either every map is 4-colorable, or a random map is almost surely a counterexample. (This much is known to be true)
"Hence the 4 color theorem is true."
This could be *really* big news.
Here's a thought that came up at work recently.
Is it possible to create a regex, that checks if a string can be converted to a floating point number (of fixed length) without truncation; in more exact terms, if
f32(str(x)) == x
for the language of your choice?
The answer to the naive question is yes, because the number of floats is finite, so we could just give a regex (0.0000000000001, 0.00000000000002, etc.). I'm interested in a "human-readable" regex.
So what're mathstodon's thoughts?
On my blog: Overthinking conference admin
Some information about how I've automated some of the process of managing a fully-online academic conference.
Another thread on a recent paper of mine "On exclusive sum labellings of hypergraphs". It's joint work with Joe Ryan at the University of Newcastle (Australia) and Zdeněk Ryjáček and Mária Skyvová at the University of West Bohemia (where I was while this work was being done).
I'm going to make the intuition toots public, but the rest unlisted to avoid timeline-pollution
However, in discovery in this case, John Abowd, the Chief Scientist at the Census Bureau, disclosed the details of their internal investigation on reconstructing the secret census records from the released statistics.
@TedOnPrivacy@twitter.com summarized it in https://desfontain.es/privacy/us-census-reconstruction-attack.html
Combinatorist (esp. graph theorist) turned Data Scientist
The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!