Concept
Binomial coefficient
The number of ways of choosing k things from n without regard to order, and the entry in row n of Pascal's triangle.
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
Pascal's triangle, in two colours
Shade the odd numbers in Pascal's triangle and a fractal appears. Nothing was designed to produce it, and the same shape arrives independently from a completely different construction.
The path folded at its first touch
Counting the walks that touch a line looks like a question about a walk's whole history. Fold each one where it first touches, and it becomes a question about where walks end up — which is a binomial coefficient, and is already known.
Named alongside it
The objects these essays reach for when they reach for this one.
Ballot problemBijectionFirst returnKummer's theoremLattice walkLucas' theoremParityPrimesRandom walkRecursionReflection principleSelf similarity