clopen.solutions

Open problems

980 registered problems.

OP-00203 Partially resolved
Exact nonnegative rank of regular polygon slack matrices
NA · extended formulations · nonnegative rank · OpenProblemsInNLA · regular polygons
OP-00273 Open
The regular-polygon Steklov conjecture
SP · AIM Open Applied Problems · isoperimetric inequalities · polygons · Steklov eigenvalues
OP-00296 Open
Pólya–Szegő polygonal Faber–Krahn conjecture
SP · AIM Open Applied Problems · Dirichlet eigenvalues · Faber–Krahn inequality · polygons
OP-00297 Open
The polygonal Payne–Pólya–Weinberger ratio conjecture
SP · AIM Open Applied Problems · Dirichlet eigenvalues · eigenvalue ratios · polygons
OP-00797 Solution claimed
Counting half-integral polygons with collinear interior lattice points
CO · AIM Open Applied Problems · lattice polygons · rational polygons
OP-00798 Solution claimed
Counting Ehrhart quasipolynomials of half-integral polygons
CO · AIM Open Applied Problems · Ehrhart quasipolynomials · rational polygons
OP-00804 Solution claimed
Exponential excursion tails for topology-preserving Ising disks
PR · AIM Open Applied Problems · rare events · self-avoiding polygons · topology-preserving dynamics