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# combinatorics

## Latest Articles

### 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.

### A New Algorithm for Graph Crossings, Hiding in Plain Sight

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory.

### Computer Scientists Attempt to Corner the Collatz Conjecture

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.

### Computer Search Settles 90-Year-Old Math Problem

By translating Keller’s conjecture into a computer-friendly search for a type of graph, researchers have finally resolved a problem about covering spaces with tiles.

### Landmark Math Proof Clears Hurdle in Top Erdős Conjecture

Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.

### ‘Rainbows’ Are a Mathematician’s Best Friend

“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.

### Rainbow Proof Shows Graphs Have Uniform Parts

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones.

### Mathematicians Begin to Tame Wild ‘Sunflower’ Problem

A major advance toward solving the 60-year-old sunflower conjecture is shedding light on how order begins to appear as random systems grow in size.