Open problems

980 registered problems.

OP-00367 Solution claimed

Smallest orders for periodic multidimensional Costas arrays

CO · AIM Open Applied Problems · Costas arrays · permutation arrays

OP-00368 Open

Absolute continuity for smooth periodic scalar elliptic operators

SP · AIM Open Applied Problems · periodic elliptic operators · spectral measures

OP-00369 Open

Removable cycles in cycle permutation graphs

CO · AIM Open Applied Problems · cycle permutation graphs · removable cycles · snarks

OP-00370 Open

Permutation snarks without five-cycles

CO · AIM Open Applied Problems · cycle permutation graphs · edge colourings · snarks

OP-00371 Open

Permutation snarks with order congruent to six modulo eight

CO · AIM Open Applied Problems · cubic graphs · edge colorings · snarks

OP-00372 Open

The sharp asymptotic facial length in girth-saturated plane graphs

CO · AIM Open Applied Problems · girth · graph saturation · plane graphs

OP-00373 Open

Polynomial-size nonobtuse tetrahedral meshes

MG · AIM Open Applied Problems · mesh generation · nonobtuse tetrahedra · triangulations

OP-00374 Open

Faber–Krahn inequality for graphene quantum dots

SP · AIM Open Applied Problems · Dirac operators · Faber–Krahn inequalities

OP-00375 Open

Are the standard quantum entropy inequalities complete?

IT · AIM Open Applied Problems · entropy cones · entropy inequalities · von Neumann entropy

OP-00376 Open

The exact real Grothendieck constant

FA · AIM Open Applied Problems · Grothendieck inequality · semidefinite relaxations · sharp constants

OP-00377 Open

Reed's bound for the chromatic number

CO · AIM Open Applied Problems · chromatic number · graph colorings

OP-00378 Open

Can bound entanglement produce a device-independent secret key?

IT · AIM Open Applied Problems · bound entanglement · quantum information · quantum key distribution

OP-00379 Open

Subpolynomial compact-set peaks of Hecke–Maass waves

NT · AIM Open Applied Problems · arithmetic quantum chaos · Maass forms · sup norms

OP-00380 Open

Global uniqueness of fine-mesh semilinear Galerkin solutions

NA · AIM Open Applied Problems · control problems · finite element methods · semilinear elliptic equations

OP-00381 Open

Simon’s multidimensional weighted square-integrability conjecture

SP · absolutely continuous spectrum · AIM Open Applied Problems · decaying potentials · Schrödinger operators

OP-00382 Open

Global convergence of the simple CRDT conformal-mapping iteration

NA · AIM Open Applied Problems · cross-ratios · numerical conformal mapping · Schwarz–Christoffel maps

OP-00383 Open

Anderson localization for the cosine skew-shift model at every coupling

SP · AIM Open Applied Problems · Anderson localization · discrete Schrödinger operators · skew-shifts

OP-00384 Open

Sharp permutation bound for triangular parts of correlation matrices

NA · AIM Open Applied Problems · correlation matrices · SOR methods · triangular truncation

OP-00385 Open

The Weinstock inequality for convex domains in a sphere

SP · AIM Open Applied Problems · convex domains · isoperimetric inequalities · Steklov eigenvalues

OP-00386 Solution claimed

Reality of the spectrum for a spherical strip with PT-symmetric boundary conditions

SP · AIM Open Applied Problems · non-self-adjoint operators · PT-symmetric operators · Robin boundary conditions

OP-00387 Open

Dynamic optimality of splay trees

CO · AIM Open Applied Problems · binary search trees · dynamic optimality · splay trees

OP-00388 Open

Optimal stable manifold widths of Besov balls

NA · AIM Open Applied Problems · Besov spaces · nonlinear approximation · nonlinear widths

OP-00389 Open

Optimal star-discrepancy lower bound for infinite sequences

NT · AIM Open Applied Problems · discrepancy · low-discrepancy sequences · quasi-Monte Carlo methods

OP-00390 Solution claimed

Unbounded first Steklov multiplicity with fixed boundary count

SP · AIM Open Applied Problems · eigenvalue multiplicities · Riemannian surfaces · Steklov eigenvalues

OP-00391 Open

Divisible point sets as unions of parallel lines

CO · AIM Open Applied Problems · direction problems · divisible codes · finite geometry

OP-00392 Open

A strongly polynomial pivot rule for the simplex method

OC · AIM Open Applied Problems · linear programming · pivot rules · simplex method

OP-00393 Open

Sunada’s no-gap conjecture for abelian covers

SP · abelian coverings · AIM Open Applied Problems · hyperbolic surfaces · spectral gaps

OP-00394 Solution claimed

A linear genus–girth bound for facial cycles

CO · AIM Open Applied Problems · facial cycles · girth · graphs on surfaces

OP-00395 Solution claimed

An optimal Weyl remainder for interior transmission eigenvalues

SP · AIM Open Applied Problems · interior transmission eigenvalues · non-self-adjoint operators · Weyl's law

OP-00396 Open

Maximum treewidth at a prescribed edge count

CO · AIM Open Applied Problems · extremal problems · tree decompositions · treewidth

OP-00397 Partially resolved

The factor-two relation between triangle deletion and packing

CO · AIM Open Applied Problems · triangle covers · triangle packings · Tuza's conjecture

OP-00398 Partially resolved

Uniformly effective algebraic multigrid for diagonally dominant systems

NA · AIM Open Applied Problems · algebraic multigrid · diagonally dominant matrices · preconditioners

OP-00399 Open

The sharp vector Riesz inequality for multidimensional potential fields

CA · AIM Open Applied Problems · Riesz transforms · sharp constants · singular integrals

OP-00400 Solution claimed

Optimal spectral signings of regular graphs

CO · AIM Open Applied Problems · graph lifts · Ramanujan graphs · signed graphs

OP-00401 Solution claimed

Non-explosion of Brownian Fleming–Viot systems in arbitrary domains

PR · AIM Open Applied Problems · Fleming–Viot particle systems · killed Brownian motion

OP-00402 Solution claimed

Additivity of entanglement of purification

MP · additivity · AIM Open Applied Problems · entanglement of purification · von Neumann entropy

OP-00403 Solution claimed

Does supercritical percolation preserve transience?

PR · AIM Open Applied Problems · Cayley graphs · percolation · random walks

OP-00404 Solution claimed

The sharp matroid secretary conjecture

OC · AIM Open Applied Problems · matroids · online algorithms · secretary problems

OP-00405 Open

The density conjecture for activated random walk on the square lattice

PR · activated random walk · AIM Open Applied Problems · interacting particle systems · self-organized criticality

OP-00406 Open

The factor-two integrality gap for asymmetric metric routing

OC · AIM Open Applied Problems · integrality gaps · linear programming relaxations · traveling salesman problem

OP-00407 Open

Consensus in the one-dimensional Axelrod model above the feature threshold

PR · AIM Open Applied Problems · Axelrod model · clustering · interacting particle systems

OP-00408 Open

Poisson nearest-neighbor spacings on almost every flat torus

NT · AIM Open Applied Problems · binary quadratic forms · flat tori · level spacings

OP-00409 Open

The exact asymptotic match fraction for independent binary sequences

PR · AIM Open Applied Problems · longest common subsequences · random sequences

OP-00410 Open

Is the variance of fair binary sequence alignment linear?

PR · AIM Open Applied Problems · longest common subsequences · sequence alignment · variance bounds

OP-00411 Open

Does a bound bipolaron ever break rotational symmetry?

MP · AIM Open Applied Problems · polarons · symmetry breaking

OP-00412 Open

Bourgain–Spencer accuracy for random elliptic media at finite contrast

AP · AIM Open Applied Problems · higher-order homogenized equations · stochastic homogenization

OP-00413 Solution claimed

Selection of the carbon-monoxide poisoning phase

PR · absorbing states · AIM Open Applied Problems · catalytic surface reactions · interacting particle systems

OP-00414 Open

Competitive exclusion in a chemostat with unequal removal rates

DS · AIM Open Applied Problems · chemostats · competitive exclusion · Lyapunov functions

OP-00415 Open

Rapid sampling of proper colorings at the ergodicity threshold

PR · AIM Open Applied Problems · Glauber dynamics · mixing times · proper colorings

OP-00416 Open

Competitive exclusion with unequal death rates

PR · AIM Open Applied Problems · competitive exclusion · multitype contact process