clopen.solutions

Open problems

1067 registered problems.

OP-00025 Open
Finitely many jumps in the integrated density of states of a linearly repetitive tiling
SP · aperiodic order · graph Laplacian · integrated density of states · linear repetitivity · locally supported eigenfunctions
OP-00026 Open
Hölder continuity of the boat–star integrated density of states at the spectral edges
SP · aperiodic order · Hölder continuity · integrated density of states · Penrose tiling · spectral edges
OP-00027 Open
Interior, edge intervals and edge regularity for the Robinson triangle tiling Laplacian
SP · Cantor spectrum · graph Laplacian · integrated density of states · Penrose tiling · Robinson triangles
OP-00314 Open
Polynomial-time proper learning of univariate Gaussian mixtures
ST · AIM Open Applied Problems · density estimation · Gaussian mixtures · proper learning
OP-00456 Open
The optimal Lieb–Oxford constant
MP · AIM Open Applied Problems · density functional theory · indirect Coulomb energies · Lieb–Oxford inequality
OP-00689 Solution claimed
Finite-density time sampling of an infinite observation window
FA · AIM Open Applied Problems · Beurling density · dynamical sampling · frames
OP-00754 Solution claimed
Sharp interactive privacy rates for spectral density estimation
ST · AIM Open Applied Problems · local differential privacy · minimax rates · spectral density estimation
OP-00766 Solution claimed
Minimax rates for private density estimation with mixed anisotropy
ST · AIM Open Applied Problems · density estimation · local differential privacy · minimax rates
OP-00935 Open
Naïve corners in products of finite groups
CO · corners · density theorems · finite groups · quasirandom groups
OP-00983 Open
Three-term progressions in F_3^n with common difference in {0,1}^n
CO · arithmetic progressions · density Hales–Jewett theorem · finite field model · restricted differences
OP-01040 Needs verification
Positive density of Hofstadter's ab − 1 set
NT · density · Erdős problems · integer sequences · multiplicative recurrences