6465 papers
This paper introduces a refined combinatorial 1-cocycle with Laurent polynomial coefficients to define refined tangle equations, providing a quantitative method to analyze knot isotopies and distinguish knot diagrams based on the solvability of these equations.
This paper investigates how algebraic invariants of edge ideals change under selective graph suspensions, demonstrating that while suspensions over minimal vertex covers consistently preserve regularity and increase projective dimension by one, suspensions over maximal independent sets exhibit uniform behavior only for paths and cycles, with a specific extremal family of paths showing increases in both regularity and the -invariant.
This paper establishes a systematic framework for constructing digraph-defined external difference families by combining graph blow-up techniques with generalized vertex labellings, resulting in new combinatorial families—including the first infinite construction for specific 2-circular external difference families—and novel results on graph labellings such as -valuations for sun graphs.
This paper disproves a homological generalization of the generalized Property R conjecture by demonstrating the existence of 2-component framed links in that surger to a connected sum of homology manifolds yet are not handleslide equivalent to a split link.
This paper investigates the minimal conditions required to establish Lipschitz and uniform bounds for sequences of bounded rough Riemannian metrics, providing counterexamples to demonstrate the sharpness of these conditions while exploring their underlying geometric intuition.
This paper introduces "Blackwells Demon," a thought experiment demonstrating that under specific restrictive conditions involving a complex environment, one can predict the direction of a random walk with a success probability greater than 1/2 by exploiting inhomogeneities in a statistically homogeneous system, analogous to how Maxwell's Demon exploits molecular speed variations.
This paper introduces a dynamic programming framework to identify extremal general polyomino chains for degree-based topological indices, specifically resolving a 2015 open problem by characterizing the chains that maximize the generalized Randić index with based on the number of squares modulo 4.
This paper proves a conjecture by Brochier, Jordan, Safronov, and Snyder that characterizes fully-dualizable and invertible -algebras within higher Morita categories, thereby identifying the specific algebraic structures that generate -dimensional and invertible topological quantum field theories.
This paper characterizes strong -matroids corresponding to orientable ribbon graphs via the new concept of pseudo-orientable ribbon graphs, establishes a geometric construction linking them to orientable graphs, and derives significant results including the Matrix--Quasi-tree Theorem, Hurwitz stability, and log-concavity for quasi-tree generating polynomials.
This paper introduces color 2-switches to characterize -colored graphs with identical color degree matrices and defines several classes of neighborhood -balanced graphs to analyze their structural properties and minimum balance numbers across various graph families.
This paper demonstrates that combining a partial pivoted Cholesky approximation with a Vecchia approximation of the residual yields an exact Vecchia approximation of the original matrix with an augmented sparsity pattern, thereby unifying low-rank and sparse inverse Cholesky approximations under a single framework.
This paper introduces FlexTrace, a novel single-pass trace estimator that accurately computes the trace of matrix functions for large symmetric positive semi-definite matrices using only matrix-vector products with the original matrix, thereby overcoming the computational expense of existing methods that require products with the function of the matrix.
This paper investigates generalized b-weakly compact operators on locally convex-solid Riesz spaces by providing new characterizations and introducing KR-spaces to establish a factorization theory analogous to that of b-weakly compact operators through KB-spaces.
This paper presents the first part of a study on the generalized Honeymoon Oberwolfach Problem by establishing existence conditions for solutions involving multiple round tables, specifically for cases with two round tables under certain modular constraints and for cases with small round tables where the total number of non-spouse seats is at most 10.
This paper demonstrates that in the general framework of -boundaries, the boundary of an infinitely ended group admitting a splitting over finite subgroups is canonically homeomorphic to the dense amalgam of the limit sets of its factor subgroups.
This paper demonstrates that while topological classification of a specific "tears of the heart" polycycle unfolding suggests four invariants, a metrical perspective reveals that for Lebesgue almost all parameter values, only two such invariants exist.
This paper presents a specialized lock-free work-stealing queue designed for a master-worker framework in mixed-integer programming solvers that leverages restricted concurrency assumptions to support native bulk operations and achieve constant-latency push performance, significantly outperforming general-purpose implementations like C++ Taskflow in batch processing scenarios.
This paper introduces a novel frequency response formulation for nonlinear systems within the Koopman operator framework, deriving a generalized complex-valued function via Laplace transforms and resolvent theory to enable Bode plot analysis under specific existence conditions.
This paper proves that for connected outerplanar graphs containing at most one or two triangles, any precoloring of two or three non-adjacent vertices can be extended to a proper 3-coloring of the entire graph.
This paper establishes a new framework of Besov spaces on bounded domains with Neumann boundary conditions to prove the local well-posedness of the Navier-Stokes equations for initial data in a space that is strictly larger than any previously considered in bounded domains.