Combinatorics of Finite Geometries is an undergraduate mathematics textbook on finite geometry by Lynn Batten. It was published by Cambridge University...

Galois geometries. Finite geometries can also be defined purely axiomatically. Most common finite geometries are Galois geometries, since any finite projective...

making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is graph...

defined purely axiomatically. Most common finite geometries are Galois geometries, since any finite projective space of dimension three or greater is isomorphic...

discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes...

of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries without the parallel postulate (non-Euclidean geometries)...

enumerative combinatorics which uses explicit combinatorial formulae and generating functions to describe the results, analytic combinatorics aims at obtaining...

Topological combinatorics Coding theory Combinatorial optimization Combinatorics and dynamical systems Combinatorics and physics Discrete geometry Finite geometry...

23–33, doi:10.1016/s0012-365x(02)00600-3 Dembowski, Peter (1968), Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Berlin...

ISBN 978-3-642-00855-9 Batten, Lynn Margaret (1986), Combinatorics of Finite Geometries, Cambridge University Press, ISBN 978-0-521-31857-0 Batten...

ISBN 9783110283600 Green, Ben (2005), "Finite field models in additive combinatorics", Surveys in Combinatorics 2005, Cambridge University Press, pp. 1–28...

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...

from areas such as algebraic geometry to solve combinatorics problems. While a few techniques that follow the framework of the polynomial method, such...

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...

specifically, over fields of interest in algebraic number theory, such as the field of rational numbers, number fields, finite fields, function fields,...

Topological Methods in Combinatorics and Geometry, Springer, ISBN 978-3-540-00362-5. Barmak, Jonathan (2011), Algebraic Topology of Finite Topological Spaces...

3,\ldots \}} Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on...

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...

problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete...

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...

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...

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...

Rotating Needles to Stability of Waves: Emerging Connections between Combinatorics, Analysis and PDE" (PDF). Notices of the AMS. 48 (3): 297–303. Katz...

Dany Breslauer and Devdatt P. Dubhashi (1995). Combinatorics for Computer Scientists John M. Sullivan (2006). Curves of Finite Total Curvature. arXiv....

classification of finite simple groups. Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic...

S2CID 119129867. Linial, Nathan (2003). "Finite metric-spaces—combinatorics, geometry and algorithms". Proceedings of the ICM, Beijing 2002. Vol. 3. pp. 573–586...

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...

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...

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...

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...