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Journal articles on the topic 'Arithmetical hyperplanes'

Author: Grafiati

Published: 31 August 2024

Last updated: 31 July 2025

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1

Bergeron, Nicolas, Frédéric Haglund, and Daniel T. Wise. "Hyperplane sections in arithmetic hyperbolic manifolds." Journal of the London Mathematical Society 83, no. 2 (2011): 431–48. http://dx.doi.org/10.1112/jlms/jdq082.

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2

Walter, Charles H. "Hyperplane sections of arithmetically Cohen-Macaulay curves." Proceedings of the American Mathematical Society 123, no. 9 (1995): 2651. http://dx.doi.org/10.1090/s0002-9939-1995-1260185-2.

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3

Ru, Min. "Geometric and Arithmetic Aspects of P n Minus Hyperplanes." American Journal of Mathematics 117, no. 2 (1995): 307. http://dx.doi.org/10.2307/2374916.

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4

Hanniel, Iddo. "Solving multivariate polynomial systems using hyperplane arithmetic and linear programming." Computer-Aided Design 46 (January 2014): 101–9. http://dx.doi.org/10.1016/j.cad.2013.08.022.

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5

Browning, Tim, and Shuntaro Yamagishi. "Arithmetic of higher-dimensional orbifolds and a mixed Waring problem." Mathematische Zeitschrift 299, no. 1-2 (2021): 1071–101. http://dx.doi.org/10.1007/s00209-021-02695-w.

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AbstractWe study the density of rational points on a higher-dimensional orbifold $$(\mathbb {P}^{n-1},\Delta )$$ ( P n - 1 , Δ ) when $$\Delta $$ Δ is a $$\mathbb {Q}$$ Q -divisor involving hyperplanes. This allows us to address a question of Tanimoto about whether the set of rational points on such an orbifold constitutes a thin set. Our approach relies on the Hardy–Littlewood circle method to first study an asymptotic version of Waring’s problem for mixed powers. In doing so we make crucial use of the recent resolution of the main conjecture in Vinogradov’s mean value theorem, due to Bourgai

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6

Andreasson, Rolf, and Robert J. Berman. "None." Journal de l’École polytechnique — Mathématiques 12 (June 17, 2025): 983–1018. https://doi.org/10.5802/jep.304.

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In our previous work we conjectured—inspired by an algebro-geometric result of Fujita—that the height of an arithmetic Fano variety 𝒳 of relative dimension n is maximal when 𝒳 is the projective space ℙ ℤ n over the integers, endowed with the Fubini-Study metric, if the corresponding complex Fano variety is K-semistable. In this work the conjecture is settled for diagonal hypersurfaces in ℙ ℤ n+1 . The proof is based on a logarithmic extension of our previous conjecture, of independent interest, which is established for toric log Fano varieties of relative dimension at most three, hyperplane ar

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7

Hoelscher, Zachary. "Semicomplete Arithmetic Sequences, Division of Hypercubes, and the Pell Constant." PUMP Journal of Undergraduate Research 4 (February 25, 2021): 108–16. http://dx.doi.org/10.46787/pump.v4i0.2524.

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In this paper we produce a few continuations of our previous work on partitions into fractions. Specifically, we study strictly increasing sequences of positive integers such that there are partitions for all natural numbers less than the floor of the sum of the first j terms divided by j, where j is greater than two. We also require that all summands be distinct terms drawn from this series of fractions. We call such sequences “semicomplete”. We find that there are only three semicomplete arithmetic sequences. We also study sequences that give the maximum number of pieces that an M dimensiona

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8

Fraser, Jonathan M., Kota Saito, and Han Yu. "Dimensions of Sets Which Uniformly Avoid Arithmetic Progressions." International Mathematics Research Notices 2019, no. 14 (2017): 4419–30. http://dx.doi.org/10.1093/imrn/rnx261.

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AbstractWe provide estimates for the dimensions of sets in $\mathbb{R}$ which uniformly avoid finite arithmetic progressions (APs). More precisely, we say $F$ uniformly avoids APs of length $k \geq 3$ if there is an $\epsilon>0$ such that one cannot find an AP of length $k$ and gap length $\Delta>0$ inside the $\epsilon \Delta$ neighbourhood of $F$. Our main result is an explicit upper bound for the Assouad (and thus Hausdorff) dimension of such sets in terms of $k$ and $\epsilon$. In the other direction, we provide examples of sets which uniformly avoid APs of a given length but still h

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9

Amerik, Ekaterina, and Misha Verbitsky. "Collections of Orbits of Hyperplane Type in Homogeneous Spaces, Homogeneous Dynamics, and Hyperkähler Geometry." International Mathematics Research Notices 2020, no. 1 (2018): 25–38. http://dx.doi.org/10.1093/imrn/rnx319.

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Abstract Consider the space M = O(p, q)/O(p) × O(q) of positive p-dimensional subspaces in a pseudo-Euclidean space V of signature (p, q), where p &gt; 0, q &gt; 1 and $(p,q)\neq (1,2)$, with integral structure: $V = V_{\mathbb{Z}} \otimes \mathbb{Z}$. Let Γ be an arithmetic subgroup in $G = O(V_{\mathbb{Z}})$, and $R \subset V_{\mathbb{Z}}$ a Γ-invariant set of vectors with negative square. Denote by R⊥ the set of all positive p-planes W ⊂ V such that the orthogonal complement W⊥ contains some r ∈ R. We prove that either R⊥ is dense in M or Γ acts on R with finitely many orbits. This

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10

Bandyopadhyay, Saptarashmi, Jason Xu, Neel Pawar, and David Touretzky. "Interactive Visualizations of Word Embeddings for K-12 Students." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 11 (2022): 12713–20. http://dx.doi.org/10.1609/aaai.v36i11.21548.

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Word embeddings, which represent words as dense feature vectors, are widely used in natural language processing. In their seminal paper on word2vec, Mikolov and colleagues showed that a feature space created by training a word prediction network on a large text corpus will encode semantic information that supports analogy by vector arithmetic, e.g., "king" minus "man" plus "woman" equals "queen". To help novices appreciate this idea, people have sought effective graphical representations of word embeddings. We describe a new interactive tool for visually exploring word embeddings. Our tool all

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11

Knutsen, Andreas Leopold, Margherita Lelli-Chiesa, and Giovanni Mongardi. "Severi varieties and Brill–Noether theory of curves on abelian surfaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 749 (2019): 161–200. http://dx.doi.org/10.1515/crelle-2016-0029.

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Abstract Severi varieties and Brill–Noether theory of curves on K3 surfaces are well understood. Yet, quite little is known for curves on abelian surfaces. Given a general abelian surface S with polarization L of type {(1,n)} , we prove nonemptiness and regularity of the Severi variety parametrizing δ-nodal curves in the linear system {|L|} for {0\leq\delta\leq n-1=p-2} (here p is the arithmetic genus of any curve in {|L|} ). We also show that a general genus g curve having as nodal model a hyperplane section of some {(1,n)} -polarized abelian surface admits only finitely many such models up t

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12

Laboureix, Bastien, and Eric Domenjoud. "On the connectedness of arithmetic hyperplanes." Theoretical Computer Science, August 2024, 114797. http://dx.doi.org/10.1016/j.tcs.2024.114797.

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13

Laboureix, Bastien, Alban Mattei, Jacques-Olivier Lachaud, and Isabelle Debled-Rennesson. "Recognition of Pieces of Arithmetic Hyperplanes Using the Stern–Brocot Tree." Journal of Mathematical Imaging and Vision 67, no. 2 (2025). https://doi.org/10.1007/s10851-025-01229-x.

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14

Ardila, Federico, Federico Castillo, and Michael Henley. "The arithmetic Tutte polynomials of the classical root systems." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AT,..., Proceedings (2014). http://dx.doi.org/10.46298/dmtcs.2447.

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International audience Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric arrangement can be computed in terms of its <i>arithmetic</i> Tutte polynomial. We compute the arithmetic Tutte polynomials of the classical root systems $A_n, B_n, C_n$, and $D_n$ with respect to their integer, root, and weight lattices. We do it in two ways: by introducing a \emphfinite field method for arithmetic Tutte polynomials, and by enumerating signed graphs with respect to six paramete

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15

Bartha, Ferenc Ágoston, Ferenc Fodor, and Bernardo González Merino. "Central Diagonal Sections of the n-Cube." International Mathematics Research Notices, October 17, 2020. http://dx.doi.org/10.1093/imrn/rnaa254.

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Abstract We prove that the volume of central hyperplane sections of a unit cube in $\mathbb{R}^n$ orthogonal to a main diagonal of the cube is a strictly monotonically increasing function of the dimension for $n\geq 3$. Our argument uses an integral formula that goes back to Pólya [ 20] (see also [ 14] and [ 3]) for the volume of central sections of the cube and Laplace’s method to estimate the asymptotic behavior of the integral. First, we show that monotonicity holds starting from some specific $n_0$. Then, using interval arithmetic and automatic differentiation, we compute an explicit bound

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16

Bath, Daniel. "Hyperplane Arrangements Satisfy (Un)Twisted Logarithmic Comparison Theorems, Applications to $\mathscr {D}_{X}$ -modules." Forum of Mathematics, Pi 12 (2024). http://dx.doi.org/10.1017/fmp.2024.17.

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Abstract For a reduced hyperplane arrangement, we prove the analytic Twisted Logarithmic Comparison Theorem, subject to mild combinatorial arithmetic conditions on the weights defining the twist. This gives a quasi-isomorphism between the twisted logarithmic de Rham complex and the twisted meromorphic de Rham complex. The latter computes the cohomology of the arrangement’s complement with coefficients from the corresponding rank one local system. We also prove the algebraic variant (when the arrangement is central), and the analytic and algebraic (untwisted) Logarithmic Comparison Theorems. Th

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17

Agrinsoni, Carlos, Heeralal Janwa, and Moises Delgado. "Toward resolution of the exceptional APN conjecture in the Kasami–Welch degree case." Journal of Algebra and Its Applications, May 20, 2025. https://doi.org/10.1142/s0219498825410269.

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An almost perfect nonlinear (APN) function is a function [Formula: see text] satisfying the property that its directional derivative at every nonzero point is two to one. APN functions arise in many areas of mathematics. For example, in cryptography, the APN function minimizes the probability of differential cryptanalysis’s success. Also, some of the curves and surfaces defined by the corresponding nonlinear functions have many rational points and have applications to Algebraic-Geometric (AG) codes [H. Janwa and R. Wilson, Hyperplane sections of Fermat varieties in [Formula: see text] in [Form

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