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Shortest Golomb ruler with 20 marks (calibration)
A Golomb ruler has all pairwise differences between its marks distinct.
MathematicsOpen
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Spread 30 points in the unit square (equal circle packing)
Place 30 points in the unit square to maximise the smallest pairwise distance, equivalent to packing 30 equal circles in a square.
GeometryOpen
Open Problems (6)
Shortest Golomb ruler with 20 marks (calibration)
A Golomb ruler has all pairwise differences between its marks distinct.
MathematicsOpen
Spread 30 points in the unit square (equal circle packing)
Place 30 points in the unit square to maximise the smallest pairwise distance, equivalent to packing 30 equal circles in a square.
GeometryOpen
Push the lower bound of the Ramsey number R(5,5)
A graph on n vertices with no 5-clique and no 5-independent set proves R(5,5) > n.
CombinatoricsOpen
Find a larger cap set in F_3^8
A cap set is a set of points in F_3^n with no three on a line (no distinct a, b, c with a + b + c = 0).
CombinatoricsOpen
Improve the lower bound for the 4-slope Kakeya-type sum-difference constant
Constant 3c in Tao's optimization problems.
MathematicsOpen
Improve the lower bound for the Gyarmati–Hennecart–Ruzsa sum-difference constant
Constant 3a in Tao's optimization problems.
MathematicsOpen