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# combinatorics

## Latest Articles

### How Math Has Changed the Shape of Gerrymandering

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

### A Very Big Small Leap Forward in Graph Theory

Four mathematicians have found a new upper limit to the “Ramsey number,” a crucial property describing unavoidable structure in graphs.

### Why Mathematicians Re-Prove What They Already Know

It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.

### The Number 15 Describes the Secret Limit of an Infinite Grid

The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer.

### Mathematicians Find Hidden Structure in a Common Type of Space

In 50 years of searching, mathematicians found only one example of a “subspace design” in a vector space. A new proof reveals that there are infinitely more out there.

### Surprise Computer Science Proof Stuns Mathematicians

For decades, mathematicians have been inching forward on a problem about which sets contain evenly spaced patterns of three numbers. Last month, two computer scientists blew past all of those results.

### Coloring by Numbers Reveals Arithmetic Patterns in Fractions

In a recent paper, two mathematicians showed that a particular pattern is unavoidable when fractions are categorized.

### Mathematicians Roll Dice and Get Rock-Paper-Scissors

Mathematicians have uncovered a surprising wealth of rock-paper-scissors-like patterns in randomly chosen dice.

### Google Researcher, Long Out of Math, Cracks Problem About Sets

On nights and weekends, Justin Gilmer attacked an old question in pure math using the tools of information theory.