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Coxeter–Dynkin Diagram
In geometry, a Harold Scott MacDonald Coxeter, Coxeter–Eugene Dynkin, Dynkin diagram (or Coxeter diagram, Coxeter graph) is a Graph (discrete mathematics), graph with numerically labeled edges (called branches) representing a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group. A class of closely related objects is the Dynkin diagrams, which differ from Coxeter diagrams in two respects: firstly, branches labeled "" or greater are Directed graph, directed, while Coxeter diagrams are Undirected graph, undirected; secondly, Dynkin diagrams must satisfy an additional (Crystallographic restriction theorem, crystallographic) restriction, namely that the only allowed branch labels are and Dynkin diagrams correspond to and are used to classify root systems and therefore semisimple Lie algebras. Description A Coxeter group is a group that admits a presentation: \langle r_0,r_1,\dots,r_n \mid (r_i r_j)^ = 1 \rangle where the are integers that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Finite Coxeter
Finite may refer to: * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked for person and/or tense or aspect * "Finite", a song by Sara Groves from the album ''Invisible Empires'' See also * Finite number (other) * Finite part (other) * Finite map (other) * Finite presentation (other) * Finite type (other) Finite type refers to several related concepts in mathematics: * Algebra of finite type, an associative algebra with finitely many generators **Morphism of finite type, a morphism of schemes with underlying morphisms on affine opens given by algebr ... * * Nonfinite (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Adjacency Matrix
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph (discrete mathematics), graph. The elements of the matrix (mathematics), matrix indicate whether pairs of Vertex (graph theory), vertices are Neighbourhood (graph theory), adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is Glossary of graph theory terms#undirected, undirected (i.e. all of its Glossary of graph theory terms#edge, edges are bidirectional), the adjacency matrix is symmetric matrix, symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory. The adjacency matrix of a graph should be distinguished from its incidence matrix, a different matrix representation whose elements indicate whether vertex–edge pairs are Incidence (graph), incident or not, and its degree matrix, whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dihedral Symmetry Domains 4
Dihedral or polyhedral may refer to: * Dihedral angle, the angle between two mathematical planes * Dihedral (aeronautics), the upward angle of a fixed-wing aircraft's wings where they meet at the fuselage, dihedral ''effect'' of an aircraft, longitudinal dihedral angle of a fixed-wing aircraft * Dihedral group, the group of symmetries of the ''n''-sided polygon in abstract algebra ** Also Dihedral symmetry in three dimensions * Dihedral kite, also known as a bowed kite * Dihedral doors, also known as butterfly doors * Dihedral prime A dihedral prime or dihedral calculator prime is a prime number that still reads like itself or another prime number when read in a seven-segment display, regardless of orientation (normally or upside down), and surface (actual display or reflecti ..., also known as a dihedral calculator prime * In Dihedral (climbing), rock climbing, an inside corner of rock See also * Anhedral (other) * Euhedral, a crystal structure * Polyhedron, a geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
