## 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 […]

## The Expected L1 Norm of Unit L2 Vectors

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 […]

## 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 […]

## 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 […]

## Just For Fun: Computing the Probability of Winning a Tournament

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.

## Some Applications of The Spicy Soup Test

Here are a few isolation inspired “applications” (in the theoretical or mathematical sense of the term) of the spicy soup combinatorial design.

## Imputing Out of Mixtures, or Un-Stirring Spicy Soup

Here is a fun combinatorial puzzle. I’ve probably seen this used to teach before, but let’s try to define or work this one from memory. I would love to hear more solutions/analyses of this problem. Suppose you have n kettles of soup labeled 0 through n-1. For our problem we […]

## What is a win vector?

From time to time we are asked “what is the company name Win-Vector LLC referring to?” It is a cryptic pun trying to be an encoding of “we deliver victory.” The story is an inside joke referring to something really only funny to one of the founders. But a joke […]

## SIGACT Review of: Combinatorics the Rota Way

SIGACT News review of: Combinatorics the Rota Way. Also found on Professor Gasarch’s page and ACM SIGACT News Volume 41, Issue 2 (paywall)