3377 papers
This paper partially answers Genevois's question regarding when hyperbolic graph braid groups arise as 3-manifold groups by demonstrating that is a 3-manifold group while for is not even quasi-isometric to one.
This paper presents a highly symmetric 6-dimensional polytope whose antipodal quotient yields a 24-vertex triangulation of , conjectured to be minimal, while also providing improved 45- and 49-vertex triangulations for .
This paper introduces combinatorics on words through the lens of low factor complexity in infinite words, exploring their minimal complexity, formalizing non-triviality, and presenting new algebraic proofs and consequences for classical theorems by Morse, Hedlund, and Tijdeman.
This paper generalizes the Micro-Transit Zoning Problem to incorporate a global budget and proposes an efficient Column Generation framework with pricing heuristics that outperforms existing enumeration-based approaches in solution quality and scalability across major U.S. cities.
This paper classifies the generating functions of genus zero lattice walks in the first quadrant with interacting boundaries by adapting a -difference equation method to show that, unlike the non-interacting case, these functions are typically hypertranscendental unless specific algebraic relations between the Boltzmann weights render them -algebraic or -rational.
This paper proposes Hadamard-NOMA, a robust downlink non-orthogonal multiple access scheme that leverages the Hadamard Transform at the source level to mitigate fading and channel state information imperfections, achieving significant bit error rate improvements over existing T-NOMA and Usman-NOMA schemes.
This paper establishes a measure-theoretic framework for constructing Arveson systems from stationary factorizing measure types, providing a rigorous characterization of spatiality and a robust mechanism for generating type III systems via infinite products, which is applied to derive explicit type III random-set systems from the zero sets of Brownian motion.
This paper establishes the foundational theory of covers and envelopes within proto-exact categories and applies these results to prove that categories of Banach modules over arbitrary Banach rings possess enough injectives.
This paper investigates the irreducible components of fixed point sets within the -character variety of a genus two surface under finite group actions, utilizing the genus two DAHA to identify geometric transitions that yield novel candidates for symmetry-reduced moduli spaces in 4d SCFTs.
This paper presents a fully device-resident, multi-GPU architecture that achieves near-zero host-device communication and 99.7% parallel efficiency through lock-free work-stealing and optimized shared-memory tiling, enabling the verification of Goldbach's conjecture up to $10^{13}$ in just 133.5 seconds on a four-GPU system with a 45.6× speedup over previous methods.
This paper demonstrates that partial differential equation propagation acts as a spectral preconditioner that improves Fourier ratio bounds, thereby enabling stable recovery of discretized fields from incomplete random spatial samples with sampling rates that are effectively independent of grid resolution.
This paper presents a simplified approach to the stable Hopf invariant by offering elementary proofs of the Cartan, Composition, and Transfer formulas, and extends these results to the stable category of -spaces for discrete groups.
This paper analyzes two coupled ODE models of political competition on probability simplices, demonstrating that a unique spectral threshold governs global stability and radicalization dynamics, where the baseline model precludes irreversible centrist decline while an extended model with disengaged voters reveals how cumulative structural shifts can trigger staircase radicalization.
This paper establishes a de Rham and Hyodo-Kato flip-flopping theorem for dual towers of rigid analytic spaces by utilizing pro-étale comparison theorems, and applies this result to prove the admissibility of the de Rham and Hyodo-Kato cohomologies of finite level coverings of Drinfeld spaces as representations of .
This paper establishes the global existence, uniform-in-time boundedness, and exponential convergence to steady states for classical solutions of two-dimensional Keller-Segel-Navier-Stokes systems with signal-dependent power-law decaying sensitivities by employing localized energy estimates and a novel interpolation inequality.
This paper establishes that the graded Ehrhart theory of unimodular zonotopes yields a -evaluation of their Tutte polynomials and characterizes their harmonic algebras as finitely generated, Cohen--Macaulay coordinate rings of arrangement Schubert varieties, thereby confirming specific conjectures by Reiner and Rhoades.
This paper introduces graph-pretzel links as a generalization of classical pretzel links and demonstrates that a specific subfamily associated with the complete graph on four vertices yields an infinite family of distinct ribbon knots that share a trivial Alexander polynomial but are distinguished by their Jones polynomials.
This paper provides an affirmative solution to an open problem posed by Brezis and Mironescu in their book *Sobolev Maps to the Circle*, demonstrating that the least mass of area-minimizing integral rectifiable currents with a smooth boundary equals the infimum of areas among smoothly immersed submanifolds sharing that boundary.
This paper provides proofs for Miyashita's characterizations of separable and Hirata separable polynomials in the general skew polynomial ring , extending the author's previous elementary proofs from the specific automorphism and derivation cases.
This paper proposes a distributed convex optimization protocol that enables portfolio managers to iteratively adjust their independent trades based on shared cost estimates, thereby significantly reducing market impact and transaction costs without requiring the disclosure of private trading strategies or direct communication between managers.