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# combinatorics

## Latest Articles

### 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?

### Computer Scientists Inch Closer to Major Algorithmic Goal

A new paper finds a faster method for determining when two mathematical groups are the same.

### Mathematicians Discover Novel Way to Predict Structure in Graphs

Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.

### First-Year Graduate Student Finds Paradoxical Set

No two pairs have the same sum; add three numbers together, and you can get any whole number.

### How Math Has Changed the Shape of Gerrymandering

New tools make it possible to detect hidden manipulation of maps.