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Combinatorics

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

December 12, 2023

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

December 6, 2023

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

November 16, 2023

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

September 8, 2023

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

August 1, 2023

The numbers count a variety of seemingly unrelated mathematical structures.

Mathematicians Solve Long-Standing Coloring Problem

July 19, 2023

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

July 7, 2023

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

June 23, 2023

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

June 22, 2023

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

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