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List Coloring Latin Squares

(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 […]

Tilting at Sign

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 […]

How often do the L1 and L2 norms agree?

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 […]

Vector Packing Vacation

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 […]

xicor for Confusion Matrices

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 […]