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-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-00076 Lean verified
Counting real Hadamard matrices
CO · Hadamard matrices · OpenProblemsInNLA · sign matrices
OP-00149 Partially resolved
A condition number of two for a sign matrix in every dimension
CO · approximate Hadamard matrices · condition numbers · OpenProblemsInNLA · sign matrices
OP-00150 Partially resolved
The optimal decay exponent for the conditioning of sign matrices
CO · approximate Hadamard matrices · condition numbers · OpenProblemsInNLA · sign matrices
OP-00185 Partially resolved
The least positive permanent of a sign matrix
CO · OpenProblemsInNLA · permanents · sign matrices
OP-00186 Partially resolved
Realizing every sign-matrix permanent with negative entries confined on or above the diagonal
CO · OpenProblemsInNLA · permanents · sign matrices