clopen.solutions

Open problems

980 registered problems.

OP-00011 Open
A 3 × 3 magic square of distinct squares
NT · Diophantine equations · magic squares
OP-00038 Partially resolved
A degree-4 Sum-of-Squares proof that ℂ⁶ has no seven mutually unbiased bases
OC · mutually unbiased bases · Randomstrasse101 · semidefinite programming · Sum-of-Squares
OP-00043 Open
A degree-4 Sum-of-Squares bound for the Paley clique number
OC · clique number · Paley graph · Randomstrasse101 · Sum-of-Squares
OP-00059 Solution claimed
Sharp norm bounds for graph matrices
PR · graph matrices · matrix chaos · random matrices · Randomstrasse101 · Sum-of-Squares
OP-00081 Lean verified
Monotonic optimal backward error along LSMR
NA · backward errors · least-squares problems · LSMR · OpenProblemsInNLA
OP-00126 Open
Subquadratic overparameterization for iterative decomposition of smoothed tensors
NA · alternating least squares · OpenProblemsInNLA · smoothed analysis · tensor decompositions
OP-00248 Solution claimed
A sum-of-squares representation for the Toeplitz commutator form
FA · Böttcher–Wenzel inequality · OpenProblemsInNLA · sums of squares · Toeplitz matrices
OP-00934 Open
A Lipschitz function on the natural numbers whose graph has no three-term progression
CO · additive squares · arithmetic progressions · combinatorics on words
OP-00946 Open
Sumsets of sets of squares grow by a power
NT · Rudin's conjecture · squares · sumsets · Λ(p) sets
OP-00947 Open
Small sets whose sumset contains the first n squares
NT · additive bases · Erdős problems · squares · sumsets
OP-00949 Open
A sum of two squares just below every large number
NT · gaps · Littlewood's problems · short intervals · sums of two squares