Vincisblog · @vincisblog
18 followers · 266 posts · Server social.anoxinon.de
PensionDan · @danpmoore
11 followers · 81 posts · Server mathstodon.xyz

So, here’s the story about how this puzzle/course came about. I have long had an interest in polytopes, and my investigations led me to learn about the tridiagonal Birkhoff polytope \( \Omega^t_n\) , and the Birkhoff polytope. In \( \Omega^t_n\), the 1s are confined to the main diagonal & the two adjacent diagonals of the permutation matrix. There are several articles about \( \Omega^t_n\), but I couldn’t find any about any other proper Birkhoff face. I thought of the story of the six blind men and the elephant, and how exploring different areas of a large object of study could yield different insights. So, I investigated other Birkhoff faces, focusing on restricting the 1 entries to sets of diagonals. \( \Omega^{xx}_n) \) wasn’t the first Birkhoff face I looked at, but I quickly realized it was inherently interesting, as the number of vertices is \(2^{n-1}\) , and the vertices have a natural naming convention that is a binary representation.
The proof of Theorem 1 (that I used; there may be others) uses . In other words, Thm 1 meets 2 of the 3 criteria Mathstodon user Rob Eastaway lists as distinguishing features of a puzzle (rather than just a math problem):
(a)…maybe it seems at first as there isn’t enough information to solve it;
(b) an aha moment

So, I posed this and following theorems as a puzzle/course because I think a lot of readers will find it fun.

#oneweirdtrick

Last updated 2 years ago

Angela · @seawall
413 followers · 3153 posts · Server mastodon.nz

Huh, CO2 monitor barely going above 635ppm when I ride the bus here in .

And the air feels ten times less stuffy and stifling than the buses back in .

What is this magic, what could it be??

Windows that open! Well I never! 🤯 😱 🌬

#otautahi #Poneke #covidisairborne #CleanTheAir #oneweirdtrick #viruseshatethis #npis

Last updated 2 years ago