Symbol n
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The cap set problem sits inside a branch of combinatorics concerned with how large a set of points can get before it is forced to contain a forbidden pattern. For cap sets the forbidden pattern is a three-term arithmetic progression: three distinct points whose coordinates sum to zero mod three. Mathematicians want to know how the size of the largest cap set in n dimensions grows as n grows, and the honest answer, as of this writing, is that nobody knows exactly — they know it grows like for some constant c , and they know c is trapped between roughly 2.2208 and roughly 2.756, a gap that has resisted closing for over a decade [ 7 , 5 ] . The lower end of that bracket is itself a short…
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Equation 8 · Technological Evolution
FunSearch Found New Mathematics Without Ever Understanding the Problem
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
The cap set problem sits inside a branch of combinatorics concerned with how large a set of points can get before it is forced to contain a forbidden pattern. For cap sets the forbidden pattern is a three-term arithmetic progression: three distinct points whose coordinates sum to zero mod three. Mathematicians want to know how the size of the largest cap set in n dimensions grows as n grows, and the honest answer, as of this writing, is that nobody knows exactly — they know it grows like for some constant c , and they know c is trapped between roughly 2.2208 and roughly 2.756, a gap that has resisted closing for over a decade [ 7 , 5 ] . The lower end of that bracket is itself a short…
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