Enumeration of Prime Parking Functions
Say $n$ cars need to park in $n$ spots, in a one-way street, but they have to announce beforehand in which spot they prefer to park. How many functions exist that allow every car to park? This is the problem of the parking functions, and I’ll discuss a way of efficiently enumerating them.
An exercise from Pope, Turbulent Flows
This post discusses exercise 6.11 (p. 205) of Turbulent Flows, the book by S. B. Pope.
The Airy function and a sequence of permutations
Let’s explore the connection between the Airy function and the integer sequence A052502.
The lognormal model and the linearization effect
The lognormal is the simplest model of the structure-function exponents in turbulence: It predicts quadratic exponents. However, a quadratic function is not a realistic model for turbulence. This post discusses how a minimum Holder exponent changes this picture, linearizes the lognormal model, and may resolve this contradiction.