(Still on my math streak.) 1994 had an exciting moment when Fred Galvin solved the 1979 Jeff Dinitz conjecture on list-coloring Latin squares. Latin squares are a simple predecessor to puzzles such as Soduko. A Latin square is an n by n grid of the integers 0 through n-1 (called […]
The proof technique for “How often do the L1 and L2 norms agree?” used as a lemma a characterization of the L1 norm of n-dimensional vectors chosen uniformly with L2 norm equal to 1. For a n-dimensional vector with unit L2 norm we can see L1 norms as small as […]
Establishing the “L1L2 AUC” equals 1/2 + arctan(1/sqrt(π – 3)) / π (≅ 0.8854404657887897) used a few nifty lemmas. One of which I am calling “the sign tilting lemma.” The sign tilting lemma is: For X, Y independent mean zero normal random variables with known variances sx2 and sy2, what […]
Turns out that I am still on a recreational mathematics run. Here is one I have been working on, arising from trying to explain norms and data science. Barry Rowlingson and John Mount asked the following question. Generate vectors v1 and v2 in Rn with each coordinate generated IID normal […]
Just coming back from a vacation where I got some side-time to work some recreational math problems. One stood out, packing vector sums by re-ordering. I feel you don’t deeply understand a proof until you try to work examples and re-write it, so here (for me) it is: Picking Vectors […]
Taking a break from weekend’s Elden Ring gaming to work out the probability of winning a tournament. The article can be found here: Some Math Inspired by Losing in Elden Ring. It is a variation on a “persuasion by calculation of examples” style I am working on.
I have a new theoretical finance note up: an appreciation of Cover’s universal portfolio in Python.
We have found that for 2 by 2 confusion matrices (a common summary relating the relation between categorical variables) the expected value of the xicor coefficient of correlation specializes into the re-normalized square of the determinant! One can summarize how a 0/1 variable x relates to a 0/1 variable y […]
For no good reason I decided to work out what shape minimized the tension at the attachment points of a draped cable. It turns out to be a lot droopier than one might expect. All of the details of the calculation using sympy can be found here.
I have a new math chalk talk up: The Game of Infinity Questions. This is back to establishing the “reasonableness” of Kolmogorov’s Axiom of continuity (in his actual formulation of his axiomatization of probability). Remember, his argument is “it is a bit off to have strong opinions on infinite processes, […]