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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.”
Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.
At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.
David Conlon and Asaf Ferber have raised the lower bound for multicolor “Ramsey numbers,” which quantify how big graphs can get before patterns inevitably emerge.
We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”
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