Catalan number - Wikipedia
The C5 = 42 noncrossing partitions of a 5-element set (below, the other 10 of the 52 partitions) In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after the French-Belgian mathematician Eugène Charles Catalan, though they were previously discovered in the 1730s by
Cayley graph - Wikipedia
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group,[1] is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley), and uses a specified set of generators for the group. It is a central tool in combinatorial and geometric group theory. The structure and symmetry
Heisenberg group - Wikipedia
In mathematics, the Heisenberg group , named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form under the operation of matrix multiplication. Elements a, b and c can be taken from any commutative ring with identity, often taken to be the ring of real numbers (resulting in the "continuous Heisenberg group") or the ring of integers (resulting in the "discrete Heisenbe
Light's associativity test - Wikipedia
In mathematics, Light's associativity test is a procedure invented by F. W. Light for testing whether a binary operation defined in a finite set by a Cayley multiplication table is associative. The naive procedure for verification of the associativity of a binary operation specified by a Cayley table, which compares the two products that can be formed from each triple of elements, is cumbersome. L
Wallpaper group - Wikipedia
Example of an Egyptian design with wallpaper group p4m A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art, especially in textiles, tiles, and wallpaper. The simplest wallpaper group, Group p1, ap
Borromean rings - Wikipedia
In mathematics, the Borromean rings[a] are three simple closed curves in three-dimensional space that are topologically linked and cannot be separated from each other, but that break apart into two unknotted and unlinked loops when any one of the three is cut or removed. Most commonly, these rings are drawn as three circles in the plane, in the pattern of a Venn diagram, alternatingly crossing ove
Morse theory - Wikipedia
"Morse function" redirects here. For anharmonic oscillators, see Morse potential. In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differentiable function on a manifold will reflect the topology quite directly. Morse
Numerology - Wikipedia
For the concept in Ismailism, see Numerology (Ismailism). For the wireless communication term, see Numerology (wireless). For branch of mathematics concerning integers, see Number theory. Numerorum mysteria (1591), a treatise on numerology by Pietro Bongo and his most influential work in Europe[1] Numerology (known before the 20th century as arithmancy) is the belief in an occult, divine or mystic
Exotic sphere - Wikipedia
In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. That is, M is a sphere from the point of view of all its topological properties, but carrying a smooth structure that is not the familiar one (hence the name "exotic"). The first exotic spheres were constructed by Joh
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Spin group - Wikipedia
Outline of algebraic structures - Wikipedia
Quaternion group - Wikipedia
Presentation of a group - Wikipedia
Conjugacy class - Wikipedia
Group cohomology - Wikipedia)
Chirality (mathematics) - Wikipedia
Coxeter–Dynkin diagram - Wikipedia
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Orientability - Wikipedia