Combinatorics

Play this simple math game with your friends to gain insights into fundamental principles of graph theory.

A surprising new solution to Leonhard Euler’s famous “36 officers puzzle” offers a novel way of encoding quantum information.

A new paper shows how to create longer disordered strings than mathematicians had thought possible, proving that a well-known recent conjecture is “spectacularly wrong.”

New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.

The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.

Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it.

The mathematician Federico Ardila takes a creative approach to the search for useful answers hiding among inconceivably huge numbers of possible ones.