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# combinatorics

## Latest Articles

### The Surprisingly Simple Math Behind Puzzling Matchups

If Anna beats Benji in a game and Benji beats Carl, will Anna beat Carl?

### The Year in Math

Landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

### A Triplet Tree Forms One of the Most Beautiful Structures in Math

The Markov numbers reveal the secrets of irrational numbers and the patterns of the Fibonacci sequence. But there’s one question about them that has resisted proof for over a century.

### ‘A-Team’ of Math Proves a Critical Link Between Addition and Sets

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”

### The Astonishing Behavior of Recursive Sequences

Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians.

### The Biggest Smallest Triangle Just Got Smaller

A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square.

### Ninth Dedekind Number Found by Two Independent Groups

The numbers count a variety of seemingly unrelated mathematical structures.

### Mathematicians Solve Long-Standing Coloring Problem

A new result shows how much of the plane can be colored by points that are never exactly one unit apart.

### The Lawlessness of Large Numbers

Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?