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Research papers
All 180 papers →Complete-result manuscripts from the Open Math Problems programme, each with the PDF, LaTeX source, a public verification report and a DOI. Unrefereed preprints by Alper Ferudun.
- EP-278 · Complete proofAn Exact Fixed-Parameter Algorithm for Extremal Unions of Residue Classes
- AIM-GEOMETRY-0175 · Complete negative answerComplex Sectional Curvature Blow-Up under Circle Cheeger Collapse
- AIM-TOPOLOGY-0102 · Complete counterexampleA Four-Point Counterexample to Excision for Directed Cubical Homology of Closure Spaces
- AIM-DYNAMICAL_SYSTEMS-0005 · Complete negative answerMaximal Generic Iterated Galois Images Do Not Determine p-Adic Julia Sets
- AIM-COMBINATORICS-0233 · Complete proofPower-Saving Lower Bounds for Additive Bases of Polynomial Sequences
- AIM-DYNAMICAL_SYSTEMS-0095 · Complete proofRamification Portraits of Rigid Lattès Maps
Show all 180 papersShow fewer
- AIM-GEOMETRY-0263 · Complete proofA Compactness Obstruction to Linear Growth Along Null Geodesics
- AIM-COMBINATORICS-0230 · Complete counterexampleLacunary Counterexamples to a Distinct-Summand Freiman Container Problem
- AIM-GEOMETRY-0274 · Complete counterexampleParallel Nilpotent Endomorphisms Without Parallel Null Vectors
- AIM-ALGEBRAIC_NUMBER_THEORY-0109 · Complete counterexampleA Positive-Rank Elliptic Curve with No Dense Prime
- AIM-FUNCTIONAL_ANALYSIS-0027 · Complete proofForcing Absoluteness of Minimal and Maximal C∗-Tensor Products
- AMR-011-0025 · Complete proofA Free-Uniform-Spanning-Forest Proof of Finite-Index Multiplicativity
- AIM-PROBABILITY-0126 · Complete proofA Slice–Riesz–Bochner Characterization of Joint Brown Determinant Functions
- AIM-ANALYSIS-0015 · Complete proofThe Spectrum of the Hilbert Matrix on Power-Weighted ℓ² Spaces
- AIM-GEOMETRIC_GROUP_THEORY-0027 · Complete proofFree-by-Cyclic Groups with Unboundedly Many BNS Component Orbits
- AIM-GEOMETRY-0195 · Complete proofAngle-Data Reconstruction for Triangulated Polyhedral Surfaces and a Genus Deficit
- AIM-TOPOLOGY-0203 · Complete proofVariable Critical Exponents on a Fixed Free-Deck Regular Cover
- AMR-011-0004 · Complete proofAdjoining a Haar-Generic Matrix to a Parabolic-Free Subgroup of SL₂(Qₚ)
- AIM-DYNAMICAL_SYSTEMS-0011 · Complete proofMaximal Finite-Set Stabilizers in Thompson's Group T
- AIM-PROBABILITY-0111 · Complete negative answerNonuniformity of Free-Gradient Heat Semigroups under Finite Fisher Information
- AIM-ARITHMETIC_GEOMETRY-0067 · Complete affirmative answerA Seventeen-Dimensional Component of the Hilbert Scheme of Eighteen Points on an Integral Curve
- AIM-ARITHMETIC_GEOMETRY-0078 · Complete proofA Generically Nonreduced Component for Hilbert Function (1,4,10,10)
- AIM-ALGEBRAIC_GEOMETRY-0125 · Complete proofSmooth Hypersurfaces Beyond the Chevalley-Warning Range over Prime Fields
- AIM-REPRESENTATION_THEORY-0023 · Complete negative answerQuantum Symmetric Algebras on Multiple Standard Copies: Structure and Categorical Non-Equivalence
- AIM-SEVERAL_COMPLEX_VARIABLES-0010 · Complete proof (stated special case)An Explicit Rational Homotopy from the Faran Map to a Linear Map in Target Dimension Four
- KOU-21.68 · Complete counterexampleA Semi-Abelian Group of Order 768 That Is Not an M-Group
- OWR-12861-021 · Complete negative answerDirac Graphs Without a Spanning Near-Square of an Odd Cycle: A Negative Answer to a Question of Heinig
- KOU-21.76 · Complete affirmative answerExplicit Closed Elementary Nets That Cannot Be Completed, Including Fields of Transcendence Degree One
- OWR-16164-019 · Complete negative answerA Counterexample to a Conjecture of Sportiello on Coloured Permutations in Convex Shapes
- OWR-1782-009 · Complete counterexample (all-n form)Small Counterexamples to the All-n Form of the Exact Codegree Conjecture for Tight Hamiltonian Cycles
- OWR-14299577-018 · Complete proofDifferences of Signed Representatives: Sharp Answers to Two Questions of Bernert and Arala Santos
- AIM-LOGIC-0084 · Complete counterexample (specified presentation)Sharp Computability Bounds for Nonforking Sections
- AIM-LINEAR_ALGEBRA-0012 · Complete theorem (D+a branch)Weighted Root Deletions and Coefficientwise Toeplitz Positivity
- AIM-COMBINATORICS-0177 · Complete counterexample (fixed label order)A Six-Vertex Counterexample to Vertex-Averaged Ordered Reachability
- AIM-REPRESENTATION_THEORY-0102 · Complete obstruction (three explicit families)A Degree-24 Obstruction to Hopf Structures on Symmetric-Group Supercharacter Spaces
- AIM-COMPUTATION-0073 · Complete scoped theorems (closed model)Strict Likelihood Multimodality and Septic Equations for Two-Component Birkhoff Models
- AIM-PROBABILITY-0108 · Complete scoped polynomial theoremsPolynomial Rigidity and a Sharp Degree Bound for Free Quadratic Variation
- AIM-REPRESENTATION_THEORY-0007 · Complete all-rank fixed-vector proofCompact-Unit Types and Fixed Vectors for Symplectic Similitudes
- AIM-PROBABILITY-0027 · Complete finite-system comparison theoremExplicit Stationary Comparisons for Join-the-Shortest-Queue Approximations
- AIM-ANALYSIS-0138 · Complete zero-location theoremsSharp Zero Regions and Hurwitz Criteria for BMV Trace Polynomials
- AIM-ANALYSIS-0089 · Complete symmetric-weighing theoremSharp Induced-Norm Paving for Symmetric Weighing Matrices
- AIM-ANALYSIS-0164 · Complete normalized-covariance criterionA Diagonal-Jet Criterion for Normalized Gaussian Analytic Covariances
- AIM-ALGEBRAIC_NUMBER_THEORY-0111 · Complete low-degree Hilbert-locus theoremLow-Degree Curves and Smooth Hilbert Loci on the Fermat Fourfold
- AIM-COMBINATORICS-0093 · Exact law and five-cycle counterexampleB-Spline Laws and Nonreal Zeros for Weighted-Cycle Internal DLA
- OPG-46575 · Complete negative answerA Negative Answer to Melnikov's Valency-Variety Problem
- OWR-17474-010 · Complete negative answerA Negative Answer to Bäumler's Question on the Number of Spin-Glass Ground States
- OWR-15428-015 · Complete negative answer and characterizationWhen Is the Set of Non-Completable Partial Probability Tensors Convex?
- OWR-4138-001 · Complete proofA Proof of the Nichols–Stolz Conjecture on the Almost-Sure Spectrum of the Bernoulli Displacement Model
- OWR-730-009 · Conditional resolution (ETH)The Exact Complexity of ε-Dense Steiner Tree
- OWR-14298808-012 · Complete proofThe Critical Window for High-Dimensional Limits of Hyperbolic Poisson k-Plane Processes
- OWR-17290-002 · Complete proof (complete setting)Essential Self-Adjointness of the Laplace–Beltrami Operator for a Family of Non-Regular Almost-Riemannian Structures
- OWR-14298367-003 · Complete proofShadowing and Generalized Hyperbolicity for Dissipative Composition Operators without Bounded Distortion
- AIM-OTHER-0001 · Complete rooted-forest linear-space algorithmFull Linear Homomesy Spaces for Rowmotion on Rooted Forests
- AIM-COMPUTATION-0025 · Explicit exponential multimodality boundsExponential Rarity of Multiple Likelihood Modes in Bivariate Seemingly Unrelated Regression
- AIM-COMBINATORICS-0209 · Effective density characterizationA Finite Gap Bound for Local Progression-Free Density
- OPG-37325 · Logarithmic bounds and negative answerLogarithmic Equivalence Covers of Powers of Cycles
- AIM-PROBABILITY-0009 · Exact forest and cycle inference countsBidirectional Inference Counts on Forests and Cycles
- AIM-OTHER-0060 · Finite induced subgraph realizationFinite Bipartite Graphs as Induced Subgraphs of Subfactor Principal Graphs
- OWR-14299088-013 · Complete counterexampleA Negative Answer to a Question of Basu and Perrucci on Two Multi-Affine Polynomials
- OWR-11578-001 · Complete counterexampleA Negative Answer to Harrach's Question on the Potential Map in the Unified Eddy-Current Formulation
- OWR-13498-011 · Complete proofThe Ford-Circle Packing Has Maximum Area: An Answer to a Question of Propp and Kenyon
- AMR-090-0002-0003 · Proof of two Ramassamy conjecturesEuler Numbers Modulo Powers of Two and Arnold's Sequence: Proof of Two Conjectures of Ramassamy
- AMR-096-0015 · Sharp asymptotics and range counterexampleExcursion Lengths in a Uniform Eulerian Circuit of the Complete Graph: Aldous's Conjecture Holds if and only if i = o(n3/2)
- OWR-14299911-029 · Complete corner-peeling counterexampleA Counterexample to a Corner-Peeling Conjecture for Subcomplexes of ℤ3
- OWR-1323-008 · Partial answer (scoped theorems)Hypercyclic Subspaces on ω and a Partial Answer to a Question of Petersson
- OWR-15436-004 · Partial answer (scoped theorems)Multistationarity of the Altan-Bonnet–Germain Kinetic-Proofreading Network: A Partial Answer to a Question of Rendall
- OWR-15428-014 · Partial answer (degree in classified cases)Partial Results on the Degree of the Algebraic Boundary in Rank-One Tensor Completion
- AMR-021-0015 · Complete counterexampleA Reciprocal-Block Counterexample to the Forsgård–Shapiro Coefficient-Parity Bound
- AMR-021-0014 · Complete counterexampleA Positive-Coefficient Counterexample to the Weighted Forsgård–Shapiro Parity Bound
- AMR-021-0016 · Complete criterionA Finite Moment-Cone Criterion for Derivative-Root Configurations
- OWR-13678-010 · Complete answer (exact dimension formula)The Dimension of Trivariate C¹ Splines on Generic Bipyramid Cells
- OWR-12697711-015 · Complete answer (all loopless matroids)The Amoeba Dimension of an Arbitrary Loopless Matroid
- AMR-050-0041 · Complete proof (least period N>4)A Telescoping Formula for Evolute Areas in Elliptic Billiards
- OWR-2489-009 · Complete counterexampleCounterexamples to Conforti's Subtree Conjecture for Mixed-Integer Bipartite Covers
- OWR-1452-024 · Negative answer (Q̄ case open)Counterexamples over F̄p to a Generic Equivalence Problem of Kraft and Russell
- OWR-13750332-001 · Complete proof (both conjectures)Star Transforms Without Type 2 Singular Directions and Conflitti's Conjecture on Elementary Symmetric Polynomials
- OWR-1703876-006 · Partial answer (question 1 solved, sharp)A Proof of Paták's kb+1 Conjecture for Constrained Stars, with Improved Bounds for Complete Graphs
- OWR-15208-008 · Complete negative answerThe Conformal Parametrization of Nonnegatively Curved Surfaces Is Not a Homeomorphism at Integer Smoothness
- OWR-14298580-008 · Complete negative answer (computer-assisted)A Negative Answer to the Strong Geography Question of Alfieri and Binns
- OWR-4798-013 · Complete affirmative answerThe Klee–Novik Complexes B(i,d) Triangulate Si × Bd−i−1
- OWR-3389-016 · Complete negative answerThe Harrell–Stubbe Gap Inequality for Dirichlet Eigenvalues Is Never Saturated
- OWR-1195-004 · Complete negative answerKernels of Signature Operators Twisted by Almost Flat Bundles Are Not Homotopy Invariant
- OWR-3385-008 · Complete proofA Proof of the Below–Krummeck–Richter-Gebert Conjecture on Cyclic Determinant Quotients
- OWR-9790358-016 · Partial answer (quadrilaterals complete)Algebraic Relations Among Mean Value Coordinates: A Complete Answer for Quadrilaterals and Partial Results for Larger Polygons
- AMR-046-0027 · Partial answer (existence and small cases)Gasull's Finite Moment Problem for Polynomials with Few Monomials
- OWR-17135-036 · Partial answer (scoped theorems)Combinatorial Spheres inside Spheres on the Same Vertex Set: Partial Results on a Question of Santos
- AMR-014-0019 · Partial answer (scoped theorems)Isolated Real Zeros of Sums of Squares: Quaternary Forms and Quinary Quartics
- AMR-050-0048 · Counterexample and corrected formulaA Focal Inversion Area Ratio for Four-Periodic Elliptic Billiards
- AMR-050-0025 · Complete proofFocal Antipedal Centroids of Rectangles Circumscribed about an Ellipse
- AMR-050-0026 · Complete proofStationary Focal Antipedal Centroids for Even Elliptic Billiard Periods
- OWR-14299906-003 · Negative answer (general case)On a Question of Freslon, Gerontogiannis and Skalski about Quantum Isometries of Cuntz–Krieger Algebras
- OWR-1275-010 · Complete answerComponents and Cohomology of Fock's Baby Teichmüller Space
- OWR-782-001 · Complete proofExtremal Modular Forms Modulo p and a Conjecture of Bannai, Koike, Shinohara and Tagami
- OWR-17294-017 · Negative answer (counterexamples)The Quantum Symmetriser of a Yang–Baxter Solution Need Not Be a Quasi-Isomorphism
- OWR-13497-006 · Complete answerAll Incorrect Equilibria of the Planar Four-Agent Formation Law Are Unstable
- OWR-11786-023 · Complete counterexampleA Negative Answer to a Question of Santos on the Dual Diameter of Surfaces with Boundary
- AMR-050-0068 · Complete scoped proofEqual Focal Inverted Pedal Areas Can Vanish in Elliptic Billiards
- AMR-050-0069 · Complete proofIsogonal Conjugacy and Equal Focal Inverted Pedal Areas
- AMR-050-0001 · Complete counterexamplesFour-Periodic Counterexamples to Two Elliptic Billiard Invariants
- AMR-050-0019 · Complete counterexampleNonconstant Antipedal Area Ratios in Four-Periodic Elliptic Billiards
- AMR-050-0021 · Complete scoped proofFocal Pedal-Antipedal Area Products in Elliptic Billiards
- AMR-050-0012 · Complete scoped proofCenter-Pedal Area Products in Elliptic Billiards
- AMR-050-0014 · Complete scoped proofOuter-Pedal Area Products in Elliptic Billiards
- AMR-050-0027 · Complete scoped proofSteiner-Centroid Pedal Area Ratios in Elliptic Billiards
- AMR-050-0007 · Complete scoped proofFocal Distance Products of Outer Elliptic Billiard Polygons
- AMR-050-0023 · Complete scoped proofOriginal Antipedal Centroids in Elliptic Billiards
- AMR-050-0029 · Complete scoped proofInner Steiner Pedal Ratios and Exceptional Zero-Area Families
- AMR-050-0036 · Complete scoped proofA Six-Periodic Zero of Focal Outer-Antipedal Area
- AMR-050-0044 · Complete scoped proofFocal Inversion Area Products in Elliptic Billiards
- AMR-050-0046 · Complete scoped proofFocal Inversion Area Ratios in Elliptic Billiards
- AMR-050-0062 · Complete proofProducts of the Two Focal Inversion Areas in Elliptic Billiards
- AMR-050-0053 · Complete adjacent-conjecture counterexampleA Pentagonal Counterexample to a Poncelet Squared-Side Criterion
- AIM-GEOMETRIC_GROUP_THEORY-0134 · Exact limit and finite-CW counterexampleExact Heisenberg Determinant Limits and Tower-Dependent Homological Torsion
- OWR-15212-005 · Complete negative answerA Negative Answer to Wolansky's Question on Mutually Dominating Multiphase Measure Spaces
- OWR-12723-008 · Complete answer (on the square)The Sharp Hexagonal Constant in Steinerberger's Geometric Uncertainty Principle on the Square
- OWR-2040-002 · Counterexamples (Conjecture 2 first refuted by Kriebel)Failures of Theorem 1 and Conjecture 3 in Knudson's Persistence–Gradient Abstract, and a Corrected Form of Conjecture 2 after Kriebel
- OWR-16766-004 · Complete counterexampleA Negative Answer to the Kadu–van Leeuwen Conjecture on Dual Binary Tomography
- OWR-15428-003 · Complete negative answerSeigal's Conjecture on Gram Determinants of Real Binary Tensors Fails for n ≥ 4
- AIM-GEOMETRY-0036 · Counterexample and corrected fixed-point proofBalanced Laurent Potentials for Finite Cluster Actions
- AMR-103-0226 · Complete affirmative answerKnots with Signature 4 and Determinant 4k+1: An Answer to a Question of Shinohara
- AIM-GEOMETRY-0250 · Counterexample and sufficient descent criterionMinimal Geodesics under Finite Covers
- AMR-099-0003 · Complete affirmative answerEquilibria of Inverse-Square Repulsion on the Line Are Arithmetic Progressions
- AIM-PROBABILITY-0131 · Bounded-tracial theoremFourier Shadows and Tracial Free Infinite Divisibility
- AIM-ALGEBRAIC_GEOMETRY-0289 · Presentation-independence theoremPresentation Independence of Ambient Adjoint Cartier Algebras
- AMR-022-7062 · Complete negative answerScales of Convergent Series and the Null Ideal: An Answer to Hinkkanen's Problem 7.62
- AMR-022-2045 · Complete affirmative answer (computer-assisted)The Equation J0(z) = 1 Has at Most One Solution on Each Ray: An Answer to a Question of Zalcman
- AMR-066-0018 · Complete counterexampleNonflat Metrics with Nonnegative Scalar Curvature That Are Flat at Infinity: A Counterexample to a Conjecture of Gromov
- AIM-LINEAR_ALGEBRA-0007 · Regular-loop logarithm counterexampleRegular Totally Nonnegative Loops Without Entire Matrix Logarithms
- AMR-036-0044 · Partial answer (new negative cases)Open Sets of Linear Systems with n = mp That Are Not Stabilizable by Static Output Feedback: New Cases of a Problem of Eremenko
- KP-1.19 · Affirmative answer (written proof of a recorded result)Asymmetric Hyperbolic Knots Detect Mapping Classes of 3-Manifolds: A Written Proof for a Problem of the K3 List
- AMR-042-0001 · Complete answer (M = 6 for every prime)The Exact Order of Mixing in a Problem of Ward: A Seven-Term Polynomial with No Sparser Multiple
- AIM-TOPOLOGY-0276 · Explicit Witt-family worked exampleA Genus-Two Algebraic Family with Vanishing Real Toledo Numbers and Nonzero Generic Witt Class
- AIM-COMPUTATION-0020 · Sharp conditional-ratio theoremSharp Ambiguity Bounds for Surviving Conditional Odds Ratios
- AIM-COMPUTATION-0095 · Sharp bound and unrestricted-exponent counterexampleA Sharp Obstruction to Uniform Low-Degree Tails over Finite Fields
- AMR-011-0009 · Normal-subgroup intersection counterexampleProperty tau Need Not Survive Intersections of Normal Subgroups
- AMR-103-0120 · Complete counterexample; classification by gauge groupA Conjecture of Guadagnini and Pilo on Quantum Invariants and the Fundamental Group: Counterexamples and a Classification by Gauge Group
- AMR-011-0049 · Complete scoped theoremExact Word-Map Distributions on Four-by-Four Unitriangular Groups
- AIM-PROBABILITY-0093 · Negative answer at the stated scaleUniform Height Bounds for Brownian Excursions with an Exact Area Constraint
- AIM-CONVEX_GEOMETRY-0001 · Minimum-perimeter theoremMinimum Perimeter of Central Hyperplane Sections of the Cube
- AIM-CONVEX_GEOMETRY-0045 · Octahedron minimum-volume theoremMinimum-Volume Central Slabs of the Regular Octahedron
- AIM-OTHER-0011 · Corner-factor theoremCorner Itineraries and Resonance of ASM Superpromotion
- AIM-SEVERAL_COMPLEX_VARIABLES-0028 · Zero-curve theorem and counterexampleAlgebraic Zero Curves of Homogeneous Plurisubharmonic Polynomials
- AIM-COMBINATORICS-0112 · Scoped theorem and orientation counterexampleOrientation Dependence and Exact Groups for Ridge-Routing Sandpiles
- AIM-ARITHMETIC_GEOMETRY-0050 · Scoped scheme-theoretic theoremsFrobenius Factorization Loci for Gauss Maps of Smooth Plane Curves
- AIM-COMBINATORICS-0257 · Scoped lower-bound theoremPolynomial Unit-Distance Lower Bounds over Prime Fields
- PE-1012 · Complete theorems and a new constantParity Rock–Paper–Scissors Games and the Alper Constant
- AIM-PROBABILITY-0013 · Scoped critical-point theoremCritical Points and Local Maxima of Sparse Binary Restricted Boltzmann Machines
- AIM-TOPOLOGY-0043 · Scoped quantum-torsion theoremQuantum Integer Torsion in the Skein Module of a Connected Sum of Two Solid Tori
- AMR-068-0001 · Complete four-point classificationThe Stress-Sign Stratification of Four Labeled Points in Three Dimensions
- AIM-PROBABILITY-0042 · Complete logarithm-removal theoremHitting Moving Targets on Eulerian Digraphs in O(mn) Expected Time
- AIM-COMBINATORICS-0263 · Complete one-point classificationOne-Point Extensions of Multiplicative Subgroups as Self-Sumsets
- AMR-014-0007 · Complete geometric count for (4,2)A Geometric Count of Fourth-Power Decompositions of Binary Octics
- AIM-GEOMETRY-0171 · Complete spherical convergence proofSmooth Convergence of Inverse Gauss Curvature Flow on the Two-Sphere
- KP-4.124 · Computer-assisted theorem (related result; the problem stays open)The Coxeter Group [5,3,3,3] Has No Torsion-Free Subgroup of Index 14400: A Computer-Assisted Result Related to Problem 4.124 of the K3 List
- AIM-TOPOLOGY-0275 · Complete split F4 product-surface theoremThe Quaternionic Toledo Spectrum for Split F4 over Products of Surfaces
- OPG-57403 · Complete answers (a proof and a counterexample)Two Problems of Porton on Reloids: Metamonovalued Reloids Are Monovalued, and S(S(f)) = S(f) Fails
- AIM-GEOMETRY-0038 · Complete finite-type comparison theoremA Common Positive Point for Braid Varieties
- KP-2.28 · Partial answer (explicit classes of graphs; the problem stays open)Sending Loxodromic Elements of Right-Angled Artin Groups to Pseudo-Anosov Mapping Classes: A Partial Answer to Problem 2.28 of the K3 List
- AIM-GEOMETRIC_GROUP_THEORY-0044 · Complete proofSpherical Type Is an Isomorphism Invariant of Artin Groups
- OWR-15427-019 · Complete dense-regime theoremLog-Free Supersaturation of Collinear Triples in Three-Dimensional Grids
- AMR-067-0008 · Partial answer (three further cases; one regime stays open)Volume-Minimising Projective Subspaces in Berger Projective Spaces: Three Further Cases of a Question of Gil-Medrano
- AMR-022-5039 · Partial answer (exact for p ≤ 2; bounds for p > 2)Duren's Problem on Integral Means of the Derivative of a Subordinate Function: the Radius 1/2 for p ≤ 2 and Bounds for p > 2
- AMR-044-0001 · Partial answer (periodicity criterion; periods in special cases)On the Billiard Problem of Dragović and Radnović for Two Concentric Half-Circles: A Periodicity Criterion and the Periods in Special Cases
- AIM-GEOMETRY-0111 · Complete scoped 3D theoremSoft Density Profiles Do Not Determine Vacant Percolation
- AMR-096-0008 · Partial answer (negative answers to two items as literally posed)On Aldous's Question about the Metropolis Chain on Cayley Graphs: Non-Monotonicity of the Relaxation Time
- AIM-GEOMETRY-0112 · Complete lattice theoremExact Small-Softness Stabilization of Euclidean Lattice Packings
- AMR-049 · Seven conjectures decided (four proved, one proved in corrected form, two disproved)On Seven Conjectures of Fuchs on Billiard Trajectories in Regular Polygons and Geodesics on the Regular Dodecahedron
- AIM-OTHER-0067 · Complete crossed-product theoremSharp Tensor Nilpotence Bounds for Finite Crossed Products
- AIM-ANALYSIS-0146 · Complete finite-operator theoremA Gaussian Obstruction to Uniform Mesh Bounds for Differential Operators
- OWR-8415343-001 · Answered: the estimate holds for every smooth G (explicit constants)A Composition Estimate for Fourier Series with the Supremum in Time Inside the Sum, and a Question of Chruściel
- OWR-16415-018 · Partial answer (four-holed spheres, genus 2 only)A Finite Cover of the Genus-Two Surface in Which Every Four-Holed Sphere Has Connected Preimage: A Partial Answer to a Question of D. Gekhtman
- AIM-SEVERAL_COMPLEX_VARIABLES-0021 · Complete counterexampleA Nonremovable Meromorphic Map into a Ball on a Codimension-Two Wedge
- AIM-DYNAMICAL_SYSTEMS-0042 · Complete proof (stated special case)Geometric and Arithmetic Independence of Affine Chebyshev Towers
- AMR-046-0017 · Complete special-case proofA Sharp Three-Cycle Bound for Two-Zone Affine Systems with a Virtual Focus
- AIM-COMBINATORICS-0183 · Complete special-class proofA Sharp Three-Fifths Bound for Seymour Vertices in Three-Regular Oriented Graphs
- OWR-8415347-019 · Answer for every N (no for N = 2, 3; yes for N ≥ 4); nilpotent residual of 𝒪(ON+) determinedThe Free Orthogonal Quantum Group ON+ Is Topologically Generated by SON and the Dual of a Free Group Exactly When N ≥ 4: On a Question of Freslon and the Nilpotent Residual of 𝒪(ON+)
- OWR-16163-011 · Partial answer (structure of the measure; no closed formula)The Law of the Sum of the Two Faces of Bi-Monotone Brownian Motion Has Atoms: A Partial Answer to a Question of M. Gerhold
- AIM-GEOMETRY-0315 · Complete scoped proof and exampleCyclic Vertex Groups and Integral Toric Restriction
- OWR-14299905-036 · Partial answer (two constants determined, with the extremal grids; computer-assisted)The Word-Search Constants C2(ABBB) = 8/5 and C3(ABB) = 6: On Two Questions of Schildkraut and of Halberstam and Schildkraut
- OWR-13494-011 · Complete negative answer (classification theorem)Line Configurations in ℙ3 Whose Symbolic Square Has Initial Degree α(I)+1 Are Coplanar or Pseudostars: A Negative Answer to a Question of Janssen
All Problems
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Problem 1
Multiples of 3 and 5
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Problem 2
Even Fibonacci Numbers
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Problem 3
Largest Prime Factor
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Largest Palindrome Product
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Smallest Multiple
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Sum Square Difference
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10001st Prime
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Largest Product in a Series
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Special Pythagorean Triplet
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Summation of Primes
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Largest Product in a Grid
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Highly Divisible Triangular Number
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Large Sum
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Longest Collatz Sequence
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Lattice Paths
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Power Digit Sum
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Number Letter Counts
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Maximum Path Sum I
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Problem 19
Counting Sundays
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Factorial Digit Sum
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Problem 21
Amicable Numbers
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Problem 22
Names Scores
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Problem 23
Non-abundant Sums
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Problem 24
Lexicographic Permutations
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Problem 25
1000-digit Fibonacci Number
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Problem 26
Reciprocal Cycles
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Problem 27
Quadratic Primes
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Problem 28
Number Spiral Diagonals
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Problem 29
Distinct Powers
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Problem 30
Digit Fifth Powers
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Problem 31
Coin Sums
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Problem 32
Pandigital Products
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Problem 33
Digit Cancelling Fractions
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Problem 34
Digit Factorials
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Circular Primes
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Double-base Palindromes
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