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Group-theoretic generalization of matroids
mathematics, Coxeter matroids are generalization of matroids depending on a choice of a Coxeter group W and a parabolic subgroup P. Ordinary matroids correspond
Coxeter_matroid
Abstraction of linear independence of vectors
antiexchange axiom Coxeter matroid – Group-theoretic generalization of matroids Greedoid – Set system used in greedy optimization Oriented matroid – Abstraction
Matroid
Canadian geometer (1907–2003)
the Coxeter graph, Coxeter groups, Coxeter's loxodromic sequence of tangent circles, Coxeter–Dynkin diagrams, and the Todd–Coxeter algorithm. Coxeter was
Harold Scott MacDonald Coxeter
Harold_Scott_MacDonald_Coxeter
Convex hull of indicator vectors of bases
a matroid polytope, also called a matroid basis polytope (or basis matroid polytope) to distinguish it from other polytopes derived from a matroid, is
Matroid_polytope
Minkowsi sum of line segments
hypercube. Zonotopes are intimately connected to hyperplane arrangements and matroid theory. The Minkowski sum of a finite set of line segments in R d {\displaystyle
Zonotope
American mathematician
of Coxeter matroids; it was published by Serganova and Israel Gelfand in 1987 as part of their research originating the concept of a Coxeter matroid. "Book
Vera_Serganova
Geometric structure of 8 points and 8 lines
as a matroid, whose elements are the points of the configuration and whose nontrivial flats are the lines of the configuration. In this matroid, a set
Möbius–Kantor_configuration
Pseudolines arranged largely to study arrangements of lines
fact has counterparts in the terminology of mutations on oriented matroids and Coxeter relations for reduced decomposition. Felsner and Valtr proved in
Arrangement_of_pseudolines
Branch of geometry that studies combinatorial properties and constructive methods
map colourings by Tait, Heawood, and Hadwiger. László Fejes Tóth, H.S.M. Coxeter, and Paul Erdős laid the foundations of discrete geometry. A polytope is
Discrete_geometry
Existence of a line through two points
oriented matroid with n {\displaystyle n} elements has at least 3 n / 7 {\displaystyle 3n/7} two-point lines, or equivalently every rank-3 matroid with fewer
Sylvester–Gallai_theorem
Length of a shortest cycle contained in the graph
unified in matroid theory by the girth of a matroid, the size of the smallest dependent set in the matroid. For a graphic matroid, the matroid girth equals
Girth_(graph_theory)
Soviet mathematician (1913–2009)
MR 2000133 Borovik, Alexandre V.; Gelfand, I. M.; White, Neil (2003), Coxeter matroids, Progress in Mathematics, vol. 216, Boston, MA: Birkhäuser Boston,
Israel_Gelfand
American mathematician
under the direction of Spencer Bloch. Brosnan is the 2009 recipient of the Coxeter–James Prize of the Canadian Mathematical Society. In 2003, Brosnan (in
Patrick_Brosnan
GF(4)-Representable Matroids", Journal of Combinatorial Theory, Series B, 79 (2): 247–299, doi:10.1006/jctb.2000.1963 Winners of the Coxeter–James Prize. Jim
Jim_Geelen
Branch of mathematics
including Zenodorus. Archimedes, Plato, Euclid, and later Kepler and Coxeter all studied convex polytopes and their properties. From the 19th century
Geometry
Branch of mathematics
analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex
Algebraic_geometry
British-Canadian codebreaker and mathematician (1917–2002)
and was about the subject later known as matroid theory. The same year, invited by Harold Scott MacDonald Coxeter, he accepted a position at the University
W._T._Tutte
Geometry without using coordinates
geometry has been founded, having close connection, for example, with matroid theory. Synthetic differential geometry is an application of topos theory
Synthetic_geometry
British mathematician
New York, 1994 Borovik, Alexandre V.; Gelfand, I. M.; White, Neil: Coxeter matroids. Progress in Mathematics, 216. Birkhäuser Boston, Inc., Boston, MA
Alexandre_Borovik
Swedish mathematician (born 1947)
Oriented Matroids (2nd ed.). Cambridge University Press. ISBN 0-521-77750-X. Björner, Anders; Brenti, Francesco (2005). Combinatorics of Coxeter Groups
Anders_Björner
Arrangement of hyperplanes
complement is fiber-type. Examples include arrangements associated with Coxeter groups of type A and B. The Orlik–Solomon algebra of every supersolvable
Supersolvable_arrangement
Sequence of spaces in linear algebra
. Filtration (mathematics) Flag (geometry) Flag manifold Grassmannian Matroid Kostrikin, Alexei I. and Manin, Yuri I. (1997). Linear Algebra and Geometry
Flag_(linear_algebra)
11613, doi:10.1016/j.jcta.2020.105273, S2CID 51775423 Luoto, K. (2008), "A matroid-friendly basis for the quasisymmetric functions", Journal of Combinatorial
Quasisymmetric_function
Study of Lie groups, Lie algebras and differential equations
classical linear algebraic groups. Special branches include Weyl groups, Coxeter groups, and buildings. The classical subject has been extended to Groups
Lie_theory
Mathematical system of orderings or sets
defining antimatroids as set systems are very similar to those of matroids, but whereas matroids are defined by an exchange axiom, antimatroids are defined instead
Antimatroid
Convex polyhedron projected from hypercube
Coxeter, H. S. M (1962). "The Classification of Zonohedra by Means of Projective Diagrams". J. Math. Pures Appl. 41: 137–156. Reprinted in Coxeter, H
Zonohedron
Branch of algebraic geometry
Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Chern Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Huygens Jyeṣṭhadeva Kātyāyana
Arithmetic_geometry
Mathematics of varieties with integer coordinates
Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Chern Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Huygens Jyeṣṭhadeva Kātyāyana
Diophantine_geometry
Geometric system of two mutually inscribed tetrahedra
the two configurations, including the fact that both are self-dual under Matroid duality. In abstract terms, the latter configuration has "points" 0, .
Möbius_configuration
Flat-sided three-dimensional shape
Bokowski, J.; Guedes de Oliveira, A. (2000), "On the generation of oriented matroids", Discrete and Computational Geometry, 24 (2–3): 197–208, doi:10.1007/s004540010027
Polyhedron
Form of entertainment in mathematics
University Press, pp. 294–301, ISBN 9780883855164. W. W. Rouse Ball and H.S.M. Coxeter (1987). Mathematical Recreations and Essays, Thirteenth Edition, Dover
Recreational_mathematics
Geometric system with a finite number of points
analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex
Finite_geometry
hypersimplex Δ d , k {\displaystyle \Delta _{d,k}} is also the matroid polytope for a uniform matroid with d {\displaystyle d} elements and rank k {\displaystyle
Hypersimplex
graph of the permutahedron. More generally, the Cayley graph of a finite Coxeter group (with the natural generators) is the edge graph of the corresponding
Graph_of_a_polytope
minimums of finite collections of polynomials. Rota's basis conjecture: for matroids of rank n {\displaystyle n} with n {\displaystyle n} disjoint bases B i
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Branch of mathematics
improved by Peano (1889), Hilbert (1899), and Veblen (1904). — H. S. M. Coxeter, Introduction to Geometry In 1901 Bertrand Russell wrote "On the Notion
Order_theory
COXETER MATROID
COXETER MATROID
Boy/Male
Shakespearean
King Henry V' and 'Henry VI, Part 1' and 'King Henry the Sixth, Part III' Duke of Exeter, uncle...
Boy/Male
Muslim/Islamic
Desirable coveted, agreeable
Boy/Male
English American
Horse herdsman. young horse;frisky.
Boy/Male
Indian
Desirable, Coveted, Pleasant
Boy/Male
Arabic, Hindu, Indian
Poeter
Surname or Lastname
English (Sussex)
English (Sussex) : unexplained.
Surname or Lastname
English
English : occupational name for someone who looked after asses and horses, from an agent derivative of Colt. Compare Coulthard.Variant spelling of German Kolter.
Boy/Male
American, British, English
Colt Herder; Keeper of the Colt Herd; Horse Herdsman; Variant of Colt; Young Horse; Frisky
Boy/Male
Muslim
Desirable, Coveted, Pleasant
Girl/Female
Arabic, Muslim
Coveted; Desired
Boy/Male
English
young horse;frisky.
Girl/Female
Muslim
Coveted, Desired
Surname or Lastname
Irish (co. Cork)
Irish (co. Cork) : reduced Anglicized form of Gaelic Mac Oitir ‘son of Oitir’, a personal name borrowed from Old Norse Óttarr, composed of the elements ótti ‘fear’, ‘dread’ + herr ‘army’.English : status name from Middle English cotter, a technical term in the feudal system for a serf or bond tenant who held a cottage by service rather than rent, from Old English cot ‘cottage’, ‘hut’ (see Coates) + -er agent suffix.Probably an Americanized spelling of German Kotter.
Boy/Male
American, Australian, British, English, Irish
Young Horse; Frisky; Part of a Plough
Surname or Lastname
English
English : variant of Coster.
Surname or Lastname
English
English : metonymic occupational name for a grower or seller of costards (Anglo-Norman French, from coste ‘rib’), a variety of large apples, so called for their prominent ribs. In some cases, it may have been a nickname (from the same word) for a person with an apple-shaped (i.e. round) head.Dutch : status name for a churchwarden, from Late Latin custor ‘guard’, ‘warden’.Variant spelling of German Koster.This name is recorded in Beverwijck in New Netherland (Albany, NY) in the mid 17th century.
Surname or Lastname
English (Devon)
English (Devon) : occupational name for a treasurer or accountant, from Middle English counter (from Old French conteor).
Boy/Male
Muslim
Desirable, Coveted, Pleasant
Boy/Male
Indian
Desirable, Coveted, Pleasant
Boy/Male
Arabic, Muslim
Agreeable; Desirable; Coveted
COXETER MATROID
COXETER MATROID
Girl/Female
American, Australian, British, Celtic, Chinese, Danish, Dutch, English, French, German, Hebrew, Romanian, Swedish
Hazelnut; Life; Light; Life Giver; Little Bird
Boy/Male
Muslim
Pioneers, Explorers, Guides
Male
Celtic
, accustomed to winning.
Boy/Male
Arabic, Hindu, Indian, Muslim, Parsi, Sikh
Crown; Dominion; Throne; Gift; Compensation; Sky; Importance
Girl/Female
Tamil
Kiss
Female
Hawaiian
Hawaiian name KEILANI means "glorious chief."
Surname or Lastname
English, southern French, German (mainly Austrian), and Hungarian
English, southern French, German (mainly Austrian), and Hungarian : from the personal name Albin (Latin Albinus, a derivative of albus ‘white’). The usual spelling of the French name is Aubin. The personal name was especially popular in Austria, Lombardy, and Savoy, where it absorbed the Germanic personal name Albuin (which is composed of the elements alb ‘elf’ + win ‘friend’). This was the name of the Lombard leader (died 572) who made himself king of northern Italy, and also of various saints, including a bishop of Brixen (Bressanone) in South Tyrol, whose name was confused with that of St. Aubin of Angers (see Aubin).
Girl/Female
Tamil
Prantika | பà¯à®°à®¨à¯à®¤à¯€à®•à®¾Â
End
Girl/Female
Indian
Courage
Boy/Male
Hindu, Indian, Traditional
Lord of Life
COXETER MATROID
COXETER MATROID
COXETER MATROID
COXETER MATROID
COXETER MATROID
n.
A piece of wood or metal, commonly wedge-shaped, used for fastening together parts of a machine or structure. It is driven into an opening through one or all of the parts. [See Illust.] In the United States a cotter is commonly called a key.
n.
A counter account. See Control.
adv.
A prefix meaning contrary, opposite, in opposition; as, counteract, counterbalance, countercheck. See Counter, adv. & a.
v. t.
To check by a counter register or duplicate account; to prove by counter statements; to confute.
a.
That may be coveted; desirable.
a.
Contrary; opposite; contrasted; opposed; adverse; antagonistic; as, a counter current; a counter revolution; a counter poison; a counter agent; counter fugue.
n.
A colter. See Colter.
n.
A flatterer; a deceiver; a cozener.
v. t.
To fasten with a cotter.
adv.
Same as Contra. Formerly used to designate any under part which served for contrast to a principal part, but now used as equivalent to counter tenor.
n.
One who covets.
n.
Same as Colter.
n.
Counter tenor; contralto.
n.
A counter tally; correspondence (in sound).
adv.
In the wrong way; contrary to the right course; as, a hound that runs counter.
n.
A counter, used in various games.
n.
A counter.
v. t.
To take a counter proof of, or a copy in reverse, by taking an impression directly from the face of an original. See Counter proof, under Counter.
n.
See Counter irritant, etc., under Counter, a.