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# combinatorics

## Latest Articles

### Mathematicians Find Structure in Biased Polynomials

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

### Mathematician Answers Chess Problem About Attacking Queens

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.

### Mathematicians Answer Old Question About Odd Graphs

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

### New Proof Reveals That Graphs With No Pentagons Are Fundamentally Different

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

### Mathematicians Settle Erdős Coloring Conjecture

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.

### Pioneers Linking Math and Computer Science Win the Abel Prize

Avi Wigderson and László Lovász won for their work developing complexity theory and graph theory, respectively, and for connecting the two fields.

### The Coach Who Led the U.S. Math Team Back to the Top

Po-Shen Loh has harnessed his competitive impulses and iconoclastic tendencies to reinvigorate the U.S. Math Olympiad program.

### A Mathematician’s Unanticipated Journey Through the Physical World

Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

### Disorder Persists in Larger Graphs, New Math Proof Finds

David Conlon and Asaf Ferber have raised the lower bound for multicolor “Ramsey numbers,” which quantify how big graphs can get before patterns inevitably emerge.