Relevant bibliographies by topics / Arithmetical hyperplanes

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Arithmetical hyperplanes'

Author: Grafiati
Published: 31 August 2024
Last updated: 31 July 2025

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Journal articles on the topic "Arithmetical hyperplanes"

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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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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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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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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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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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 > 0, q > 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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Dissertations / Theses on the topic "Arithmetical hyperplanes"

1

Laboureix, Bastien. "Hyperplans arithmétiques : connexité, reconnaissance et transformations." Electronic Thesis or Diss., Université de Lorraine, 2024. http://www.theses.fr/2024LORR0040.

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Le monde numérique est parsemé de structures mathématiques discrètes, destinées à être facilement manipulables par un ordinateur tout en donnant à notre cerveau l'impression d'être de belles formes réelles continues. Les images numériques peuvent ainsi être vues comme des sous-ensembles de Z^2. En géométrie discrète, nous nous intéressons aux structures de Z^d et cherchons à établir des propriétés géométriques ou topologiques sur ces objets. Si les questions que nous nous posons sont relativement simples en géométrie euclidienne, elles deviennent beaucoup plus difficiles en géométrie discrète
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Books on the topic "Arithmetical hyperplanes"

1

Barg, Alexander, and O. R. Musin. Discrete geometry and algebraic combinatorics. American Mathematical Society, 2014.

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2

Mathematical Legacy of Richard P. Stanley. American Mathematical Society, 2016.

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Book chapters on the topic "Arithmetical hyperplanes"

1

Jamet, Damien, and Jean-Luc Toutant. "On the Connectedness of Rational Arithmetic Discrete Hyperplanes." In Discrete Geometry for Computer Imagery. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11907350_19.

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2

Domenjoud, Eric, Bastien Laboureix, and Laurent Vuillon. "Facet Connectedness of Arithmetic Discrete Hyperplanes with Non-Zero Shift." In Discrete Geometry for Computer Imagery. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-14085-4_4.

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3

Laboureix, Bastien, and Isabelle Debled-Rennesson. "Recognition of Arithmetic Line Segments and Hyperplanes Using the Stern-Brocot Tree." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57793-2_2.

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You might also be interested in the extended bibliographies on the topic 'Arithmetical hyperplanes' for particular source types:
Journal articles
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