clopen.solutions

Open problems

980 registered problems.

OP-00031 Open
The largest discrepancy of square ±1 matrices relative to √n
CO · discrepancy theory · Randomstrasse101 · sign matrices · Spencer's theorem
OP-00051 Solution claimed
The Group Spencer conjecture
CO · discrepancy theory · Matrix Spencer · Randomstrasse101 · regular representation
OP-00055 Solution claimed
Infinitely many square ±1 matrices with discrepancy a constant factor above √n
CO · discrepancy theory · Randomstrasse101 · sign matrices · Spencer's theorem
OP-00056 Solved
The discrepancy of the Sylvester–Hadamard matrices H_k for odd k
CO · Boolean functions · discrepancy theory · Hadamard matrices · Randomstrasse101
OP-00061 Solution claimed
The Matrix Spencer conjecture
CO · discrepancy theory · Matrix Spencer · random matrices · Randomstrasse101
OP-00064 Solution claimed
The Komlós conjecture
CO · discrepancy theory · Komlós conjecture · Randomstrasse101 · vector balancing
OP-00954 Open
Weak nets of linear size for axis-parallel rectangles
CO · axis-parallel rectangles · discrepancy theory · discrete geometry · weak epsilon-nets