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combinatorics

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Blurry figures representing quantum officers are arranged in a grid against a black background.
mathematical physics

Euler’s 243-Year-Old ‘Impossible’ Puzzle Gets a Quantum Solution

By Daniel Garisto
January 10, 2022
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A surprising new solution to Leonhard Euler’s famous “36 officers puzzle” offers a novel way of encoding quantum information.

An illustration of a mathematician on a ladder stringing red and blue beads against a tiled red backdrop dotted with blue circles.
combinatorics

Mathematician Hurls Structure and Disorder Into Century-Old Problem

By Erica Klarreich
December 15, 2021
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A new paper shows how to create longer disordered strings than mathematicians had thought possible, proving that a well-known recent conjecture is “spectacularly wrong.”

An image with Lego blocks representing polynomials and their factors.
polynomials

Mathematicians Find Structure in Biased Polynomials

By Tamar Lichter Blanks
November 9, 2021
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New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.

combinatorics

Mathematician Answers Chess Problem About Attacking Queens

By Leila Sloman
September 21, 2021
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The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.

Illustration showing a graph against a purple background, with certain vertices and edges highlighted in orange.
combinatorics

Mathematicians Answer Old Question About Odd Graphs

By Kevin Hartnett
May 19, 2021
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A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.

graph theory

New Proof Reveals That Graphs With No Pentagons Are Fundamentally Different

By Steve Nadis
April 26, 2021
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Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.

Side-by-side illustrations of the same linear hypergraph. The edges of the hypergraph are colored in the illustration on the right, but not in the illustration on the left.
combinatorics

Mathematicians Settle Erdős Coloring Conjecture

By Kelsey Houston-Edwards
April 5, 2021
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Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it.

Abel Prize

Pioneers Linking Math and Computer Science Win the Abel Prize

By Kevin Hartnett
March 17, 2021
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Avi Wigderson and László Lovász won for their work developing complexity theory and graph theory, respectively, and for connecting the two fields.

Po-Shen Loh standing on a stairway in front of a colored wall outside of his office in Pittsburgh.
Q&A

The Coach Who Led the U.S. Math Team Back to the Top

By Max G. Levy
February 16, 2021
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Po-Shen Loh has harnessed his competitive impulses and iconoclastic tendencies to reinvigorate the U.S. Math Olympiad program.


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