A note on hyperseparating set systems
This paper determines the minimum sizes of -completely hyperseparating set systems for general and of $2$-hyperseparating set systems, thereby generalizing recent results by Bat'iková, Kepka, and Němec.
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math
4567 papers
Proportion of chiral maps with automorphism group and
This paper proves that as approaches infinity, the proportion of orientably-regular maps and hypermaps with automorphism groups or that are chiral tends to 1, establishing that chirality is generic for these structures.
A reverse isoperimetric inequality in three-dimensional space forms
This paper proves a sharp reverse isoperimetric inequality in three-dimensional space forms of constant curvature, demonstrating that among all -convex bodies with a fixed surface area, the -convex lens uniquely minimizes volume, thereby confirming Borisenko's Conjecture for non-zero curvature cases.
Eigenvalue accumulation for operator convolutions on locally compact groups
This paper establishes that the asymptotic accumulation of eigenvalues near unity for convolutions of indicator functions and density operators on locally compact groups occurs if and only if the group is unimodular and the underlying sets form a Følner sequence, thereby extending known results for the Heisenberg group to broader classes such as nilpotent and homogeneous Lie groups.
The W-footrule coefficient: A copula-based measure of countermonotonicity
This paper introduces the -footrule coefficient, a new copula-based measure of negative association defined as the -distance to the countermonotonic copula, establishes its theoretical relationship with Gini's gamma and Spearman's footrule, and provides a statistically rigorous rank-based estimator with proven consistency and asymptotic normality.
Optimal Embedding of Wiring Diagrams in Constrained Three-Dimensional Spaces
This paper proposes a mixed-integer linear programming framework that discretizes the three-dimensional wiring diagram problem into structured network graphs to optimize cable or pipeline routing while satisfying complex industrial constraints such as obstacle avoidance, safety distances, and constructibility.
Primitive elements in Ringel-Hall algebras of tame hereditary algebras
This paper characterizes primitive elements in the Ringel-Hall algebra of a tame hereditary algebra associated with a quiver with automorphism, providing a generalized description that improves upon previous results for tame quivers and constructing an explicit basis for the space of primitive elements via a new identity in the regular subalgebra.
Fat Lie Theory
This paper introduces the framework of "fat Lie theory" to establish a one-to-one correspondence between fat extensions and abstract 2-term representations up to homotopy, while demonstrating that fat extensions of groupoids correspond to general linear PB-groupoids and core extensions to vertically/horizontally core-transitive double groupoids, thereby upgrading existing correspondences to equivalences of categories.
Convexity of Berezin Range and Berezin Radius Inequalities via a class of Seminorm
This paper introduces a new family of -Berezin seminorms to establish refined inequalities for the Berezin radius and investigates the convexity of Berezin ranges for specific operators on weighted Hardy and Fock spaces.
Pointwise estimates for rough operators in a metric measure framework under some Ahlfors regularity conditions
This paper establishes a new pointwise estimate for rough operators in Ahlfors regular metric measure spaces by combining a subrepresentation formula involving modified Riesz potentials with a maximal function control, and subsequently derives a family of functional inequalities from this result.
WKB-asymptotics for multipoint Virasoro conformal blocks and applications
This paper derives WKB-asymptotic expressions for multipoint Virasoro conformal blocks in the comb channel on the sphere by applying the WKB method to the classical BPZ equation, validating the results against known exact solutions and AGT correspondence while demonstrating their utility for generalizing Zamolodchikov's elliptic recursion and numerically evaluating minimal string theory amplitudes.
Algorithm with variable coefficients for computing matrix inverses
This paper presents a general scheme for constructing optimal and numerically stable generalized Schultz iterative methods with variable coefficients to efficiently compute matrix inverses, supported by theoretical derivation and numerical testing.
Caveats on formulating finite elasto-plasticity in curvilinear coordinates
This paper presents a practical, step-by-step methodology for formulating finite elasto-plasticity in curvilinear coordinates using explicit basis changes rather than differential geometry, clarifying the treatment of deformation gradients, Jacobians, and shifters to enable robust finite element analysis of axisymmetric problems with large deformations.
Hyperbolic elliptic parabolic disks approximated by half distance bands
This paper investigates the geometric relationship between hyperbolic, elliptic, and parabolic disks and their supporting half-distance bands within the Beltrami–Cayley–Klein model, aiming to define and quantify their "closeness" through precise approximations of area and circumference.
Heights on toric varieties for singular metrics: Global theory
This paper establishes a toric analog of Yuan and Zhang's theory of adelic divisors to show that the arithmetic self-intersection number of a semipositive toric adelic divisor equals the integral of a concave function over a compact convex set, thereby enabling the computation of heights for toric arithmetic varieties with singular metrics.
Capacity of Non-Separable Networks with Restricted Adversaries
This paper investigates the capacity of single-source multicasting in networks with restricted adversaries, demonstrating that classical bounds are insufficient and requiring joint code design, while providing exact capacity results, improved lower bounds, and new generalizations for specific network families.
The Levi problem over generalized Hirzebruch manifolds
This paper reviews classical symmetry-based methods for solving the Levi problem and applies them to resolve the problem for generalized Hirzebruch manifolds and primary Hopf surfaces of non-diagonal type.
Kleinian hyperelliptic funtions of weight 2 associated with curves of genus 2
This paper introduces a new collection of special functions associated with complex curves of genus 2 that relate to weight 2 -functions analogously to the Kleinian -function, with the distinct advantage of being well-defined for all such curves without requiring a Weierstrass point at infinity.
Sampling Colorings with Fixed Color Class Sizes
This paper presents a polynomial-time algorithm for approximately sampling uniformly random equitable colorings when the number of colors exceeds $2\Delta$, utilizing the geometry of polynomials framework to establish a multivariate local Central Limit Theorem for color class sizes.
Central Limits via Dilated Categories
This paper introduces dilated seminorm-enriched category theory as a unifying framework for central limit theorems, establishing an abstract CLT that recovers classical results and yields novel applications in symplectic manifolds and statistical mechanics.