• Combinatorics of Finite Geometries is an undergraduate mathematics textbook on finite geometry by Lynn Batten. It was published by Cambridge University...
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  • Thumbnail for Finite geometry
    Galois geometries. Finite geometries can also be defined purely axiomatically. Most common finite geometries are Galois geometries, since any finite projective...
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  • making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is graph...
    33 KB (3,524 words) - 20:02, 6 May 2025
  • Thumbnail for Algebraic combinatorics
    defined purely axiomatically. Most common finite geometries are Galois geometries, since any finite projective space of dimension three or greater is isomorphic...
    13 KB (1,289 words) - 14:02, 16 October 2024
  • Thumbnail for Discrete geometry
    discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes...
    15 KB (1,575 words) - 05:36, 16 October 2024
  • of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries without the parallel postulate (non-Euclidean geometries)...
    102 KB (10,101 words) - 16:23, 8 May 2025
  • Thumbnail for Discrete mathematics
    enumerative combinatorics which uses explicit combinatorial formulae and generating functions to describe the results, analytic combinatorics aims at obtaining...
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  • Topological combinatorics Coding theory Combinatorial optimization Combinatorics and dynamical systems Combinatorics and physics Discrete geometry Finite geometry...
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  • 23–33, doi:10.1016/s0012-365x(02)00600-3 Dembowski, Peter (1968), Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Berlin...
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  • ISBN 978-3-642-00855-9 Batten, Lynn Margaret (1986), Combinatorics of Finite Geometries, Cambridge University Press, ISBN 978-0-521-31857-0 Batten...
    27 KB (3,319 words) - 17:55, 18 May 2025
  • ISBN 9783110283600 Green, Ben (2005), "Finite field models in additive combinatorics", Surveys in Combinatorics 2005, Cambridge University Press, pp. 1–28...
    45 KB (7,535 words) - 18:07, 22 April 2025
  • Thumbnail for Configuration (geometry)
    specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point...
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  • from areas such as algebraic geometry to solve combinatorics problems. While a few techniques that follow the framework of the polynomial method, such...
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  • Thumbnail for Arrangement of hyperplanes
    In geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space...
    13 KB (1,806 words) - 08:52, 30 January 2025
  • Thumbnail for Algebraic geometry
    specifically, over fields of interest in algebraic number theory, such as the field of rational numbers, number fields, finite fields, function fields,...
    62 KB (7,498 words) - 11:10, 27 May 2025
  • Topological Methods in Combinatorics and Geometry, Springer, ISBN 978-3-540-00362-5. Barmak, Jonathan (2011), Algebraic Topology of Finite Topological Spaces...
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  • 3,\ldots \}} Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on...
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  • Thumbnail for Arithmetic geometry
    schemes of finite type over the spectrum of the ring of integers. The classical objects of interest in arithmetic geometry are rational points: sets of solutions...
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  • problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete...
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  • integral points occurs in Chapter 28. Mordell's theorem on the finite generation of the group of rational points on an elliptic curve is in Chapter 16, and...
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  • discrete places on a meshed geometry. "Finite volume" refers to the small volume surrounding each node point on a mesh. In the finite volume method, volume...
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  • cohomology theory Extremal combinatorics a branch of combinatorics, it is the study of the possible sizes of a collection of finite objects given certain restrictions...
    71 KB (7,692 words) - 22:32, 2 March 2025
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    Rotating Needles to Stability of Waves: Emerging Connections between Combinatorics, Analysis and PDE" (PDF). Notices of the AMS. 48 (3): 297–303. Katz...
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  • Schur's theorem (category Additive combinatorics)
    Dany Breslauer and Devdatt P. Dubhashi (1995). Combinatorics for Computer Scientists John M. Sullivan (2006). Curves of Finite Total Curvature. arXiv....
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  • Thumbnail for Group theory
    classification of finite simple groups. Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic...
    39 KB (5,086 words) - 18:26, 11 April 2025
  • Thumbnail for Metric space
    S2CID 119129867. Linial, Nathan (2003). "Finite metric-spaces—combinatorics, geometry and algorithms". Proceedings of the ICM, Beijing 2002. Vol. 3. pp. 573–586...
    82 KB (11,434 words) - 17:46, 21 May 2025
  • Thumbnail for Finitely generated group
    In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination...
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  • Logical matrix (category Pages that use a deprecated format of the math tags)
    A Costas array is a special case of a permutation matrix. An incidence matrix in combinatorics and finite geometry has ones to indicate incidence between...
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  • Szemerédi–Trotter theorem (category Theorems in combinatorics)
    Szemerédi–Trotter type theorem and the sum-product estimate in finite fields". European Journal of Combinatorics. 32 (8): 1177–1181. arXiv:0711.4427. doi:10.1016/j...
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  • existence of a theory of projective geometry in which the degenerate geometries would have equal standing with the classical ones. This geometry would take place...
    32 KB (3,811 words) - 09:27, 13 May 2025