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# combinatorics

## Latest Articles

### ‘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.

### Color Me Polynomial

Polynomials aren’t just exercises in abstraction. They’re good at illuminating structure in surprising places.

### Decades-Old Computer Science Conjecture Solved in Two Pages

The “sensitivity” conjecture stumped many top computer scientists, yet the new proof is so simple that one researcher summed it up in a single tweet.

### A 53-Year-Old Network Coloring Conjecture Is Disproved

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.

### How a Strange Grid Reveals Hidden Connections Between Simple Numbers

A graduate student has helped illuminate a long-suspected connection between addition and multiplication.

### A Child’s Puzzle Has Helped Unlock the Secrets of Magnetism

People have known about magnets since ancient times, but the physics of ferromagnetism remains a mystery. Now a familiar puzzle is getting physicists closer to the answer.

### Unscrambling the Hidden Secrets of Superpermutations

A science fiction novelist and an internet commenter made breakthroughs on a longstanding problem about the number of ways you can arrange a set of items. What did they discover?