Results 11 to 20 of about 45 (44)
f$f$‐Diophantine sets over finite fields via quasi‐random hypergraphs from multivariate polynomials
Mathematika, Volume 72, Issue 2, April 2026.Abstract We investigate f$f$‐Diophantine sets over finite fields via new explicit constructions of families of quasi‐random hypergraphs from multivariate polynomials. In particular, our construction not only offers a systematic method for constructing quasi‐random hypergraphs but also provides a unified framework for studying various hypergraphs ...
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
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Circle packings, renormalizations, and subdivision rules
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract In this paper, we use iterations of skinning maps on Teichmüller spaces to study circle packings and develop a renormalization theory for circle packings whose nerves satisfy certain subdivision rules. We characterize when the skinning map has bounded image.
Yusheng Luo, Yongquan Zhang
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Determinacy on the edge of second‐order arithmetic, I
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract This is the first of two articles on the strength of m$m{}$‐Σ30$\bm{\Sigma }^0_3{}$‐determinacy for m∈N$m\in \mathbb {N}$, the strongest theories of determinacy contained in Hilbert's second‐order arithmetic (Z2)$(Z_2)$. In this article, we refute two natural conjectures on the strength of these principles in terms of inductive definability ...
J. P. Aguilera, P. D. Welch
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Coloring and density theorems for configurations of a given volume
Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.Abstract This is a treatise on finite point configurations spanning a fixed volume to be found in a single color‐class of an arbitrary finite (measurable) coloring of the Euclidean space Rn$\mathbb {R}^n$, or in a single large measurable subset A⊆Rn$A\subseteq \mathbb {R}^n$.
Vjekoslav Kovač
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New Difference Triangle Sets by a Field‐Programmable Gate Array‐Based Search Technique
Journal of Combinatorial Designs, Volume 34, Issue 1, Page 37-50, January 2026.ABSTRACT We provide some difference triangle sets with scopes that improve upon the best known values. These are found with purpose‐built digital circuits realized with field‐programmable gate arrays (FPGAs) rather than software algorithms running on general‐purpose processors.
Mohannad Shehadeh +2 more
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Plank theorems and their applications: A survey
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
William Verreault
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The dimension of well approximable numbers
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine ...
Victor Beresnevich, Sanju Velani
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Arithmetic constants for symplectic variances of the divisor function
Mathematika, Volume 71, Issue 3, July 2025.Abstract Kuperberg and Lalín stated some conjectures on the variance of certain sums of the divisor function dk(n)$d_k(n)$ over number fields, which were inspired by analogous results over function fields proven by the authors. These problems are related to certain symplectic matrix integrals. While the function field results can be directly related to
Vivian Kuperberg, Matilde Lalín
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Journal of Function Spaces, Volume 2025, Issue 1, 2025.Algebraic curves and topological sequences play a crucial role in mathematics and graph theory, serving as a bridge between geometry, algebra, and number theory. They facilitate structural analysis in various applications, including chemistry, network analysis, and computer science.
Mohammad Mazyad Hazzazi +5 more
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Cover and hitting times of hyperbolic random graphs
Random Structures &Algorithms, Volume 65, Issue 4, Page 915-978, December 2024.Abstract We study random walks on the giant component of Hyperbolic Random Graphs (HRGs), in the regime when the degree distribution obeys a power law with exponent in the range (2,3)$$ \left(2,3\right) $$. In particular, we first focus on the expected time for a random walk to hit a given vertex or visit, that is, cover, all vertices.
Marcos Kiwi +2 more
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