AI & ChatGPT searches , social queriess for REGULAR MATROID
Search references for REGULAR MATROID. Phrases containing REGULAR MATROID
See searches and references containing REGULAR MATROID!
Search references for REGULAR MATROID. Phrases containing REGULAR MATROID
See searches and references containing REGULAR MATROID!REGULAR MATROID
Matroid that can be represented over all fields
In mathematics, a regular matroid is a matroid that can be represented over all fields. A matroid is defined to be a family of subsets of a finite set
Regular_matroid
Abstraction of linear independence of vectors
In combinatorics, a matroid /ˈmeɪtrɔɪd/ is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many
Matroid
Vectors with given pattern of independence
theory of matroids, a matroid representation is a family of vectors whose linear independence relation is the same as that of a given matroid. Matroid representations
Matroid_representation
Matroid with graph forests as independent sets
In the mathematical theory of matroids, a graphic matroid (also called a cycle matroid or polygon matroid) is a matroid whose independent sets are the
Graphic_matroid
Topics referred to by the same term
(related to the regular expression) Regular map (graph theory), a symmetric tessellation of a closed surface Regular matroid, a matroid which can be represented
Regular
Abstraction of ordered linear algebra
The first appearance of oriented matroids was in a 1966 article by George J. Minty and was confined to regular matroids. Subsequently R.T. Rockafellar (1969)
Oriented_matroid
Matroid obtained by restrictions and contractions
of matroids, a minor of a matroid M is another matroid N that is obtained from M by a sequence of restriction and contraction operations. Matroid minors
Matroid_minor
Integer matrices with +1 or −1 determinant; invertible over the integers. GL_n(Z)
mean matrices that are invertible over the field. Balanced matrix Regular matroid Special linear group Total dual integrality Hermite normal form The
Unimodular_matrix
Maximal independent set of the matroid
In mathematics, a basis of a matroid is a maximal independent set of the matroid—that is, an independent set that is not contained in any other independent
Basis_of_a_matroid
Abstraction of mod-2 vector independence
matroid theory, a binary matroid is a matroid that can be represented over the finite field GF(2). That is, up to isomorphism, they are the matroids whose
Binary_matroid
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
British-Canadian codebreaker and mathematician (1917–2002)
accomplishments, including foundational work in the fields of graph theory and matroid theory. Tutte's research in the field of graph theory proved to be of remarkable
W._T._Tutte
On the number of spanning trees in a graph
also be used to determine the number of bases in regular matroids, a generalization of the graphic matroids (Maurer 1976). Kirchhoff's theorem can be modified
Kirchhoff's_theorem
British mathematician
theory. He (with others) was responsible for important progress on regular matroids and totally unimodular matrices, the four colour theorem, linkless
Paul_Seymour_(mathematician)
Matroid with complemented basis sets
In matroid theory, the dual of a matroid M {\displaystyle M} is another matroid M ∗ {\displaystyle M^{\ast }} that has the same elements as M {\displaystyle
Dual_matroid
Area of combinatorics
Thus the combinatorial topics may be enumerative in nature or involve matroids, polytopes, partially ordered sets, or finite geometries. On the algebraic
Algebraic_combinatorics
Conjecture on forbidden minors of matroids
by Tutte (1958) of the regular matroids (matroids that can be represented over all fields) it follows that a matroid is regular if and only if it is both
Rota's_conjecture
Gluing graphs at complete subgraphs
generalized from graphs to matroids. Notably, Seymour's decomposition theorem characterizes the regular matroids (the matroids representable by totally
Clique-sum
Subroutine for testing independence
mathematics and computer science, a matroid oracle is a subroutine through which an algorithm may access a matroid, an abstract combinatorial structure
Matroid_oracle
extension complexity. On the other hand, the independence polytope of regular matroids has polynomial extension complexity. The notion of extension complexity
Extension_complexity
1979 classic textbook on computational complexity theory
1007/978-3-319-44914-2_9. In P: Seymour, P. D. (June 1980). "Decomposition of regular matroids" (PDF). Journal of Combinatorial Theory, Series B. 28 (3): 305–359
Computers_and_Intractability
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)
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
Abstraction of disjoint paths in directed graphs
In matroid theory, a field within mathematics, a gammoid is a certain kind of matroid, describing sets of vertices that can be reached by vertex-disjoint
Gammoid
Graph representing faces of another graph
matroid of M. Then Whitney's planarity criterion can be rephrased as stating that the dual matroid of a graphic matroid M is itself a graphic matroid
Dual_graph
Abstraction of unicyclic subgraphs
In the mathematical subject of matroid theory, the bicircular matroid of a graph G is the matroid B(G) whose points are the edges of G and whose independent
Bicircular_matroid
American mathematician
Klee–Minty cube, the Browder–Minty theorem, the introduction of oriented regular matroids, and the Minty-Vitaver theorem on graph coloring. George Minty Jr.
George_J._Minty
Branch of geometry that studies combinatorial properties and constructive methods
Configurations Line arrangements Hyperplane arrangements Buildings An oriented matroid is a mathematical structure that abstracts the properties of directed graphs
Discrete_geometry
Algebraic encoding of graph connectivity
and number of connected components, with immediate generalizations to matroids. It is also the most general graph invariant that can be defined by a
Tutte_polynomial
Branch of discrete mathematics
Not only the structure but also enumerative properties belong to matroid theory. Matroid theory was introduced by Hassler Whitney and studied as a part
Combinatorics
Geometry with 7 points and 7 lines
theory of matroids. Excluding the Fano plane as a matroid minor is necessary to characterize several important classes of matroids, such as regular, graphic
Fano_plane
Mathematical ways to group elements of a set
geometric lattices and matroids, this lattice of partitions of a finite set corresponds to a matroid in which the base set of the matroid consists of the atoms
Partition_of_a_set
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
Set that intersects every one of a family of sets
finite sets form the basis sets of a matroid, the transversal matroid of C. The independent sets of the transversal matroid are the partial transversals of
Transversal_(combinatorics)
Intersection of two partition matroids - 6.75 Intersection of a graphic matroid and a partition matroid - 10.66 General matroid with matroid rank k {\displaystyle
Bayesian-optimal_pricing
Field extension that is not algebraic
in field extensions both form examples of finitary matroids (pregeometries). Any finitary matroid has a basis, and all bases have the same cardinality
Transcendental_extension
Natural number
nodes, 68 different degree sequences of four-node connected graphs, and 68 matroids on four labeled elements. Størmer's theorem proves that, for every number
68_(number)
American mathematician
oriented matroids; in particular, the Folkman–Lawrence topological representation theorem is "one of the cornerstones of the theory of oriented matroids". In
Jon_Folkman
Result in combinatorics and graph theory
to determine the existence of a transversal which is independent in a matroid. Hall 1986, pg. 51. An alternative form of the marriage theorem applies
Hall's_marriage_theorem
Irrational system of points and lines
inherited by any other matroid within which the Perles matroid appears as a matroid minor. In tropical geometry, this matroid has been used to separate
Perles_configuration
Combinatorial theory of mechanics and discrete geometry
rigidity of rod-and-hinge linkages is described by a matroid. The bases of the two-dimensional rigidity matroid (the minimally rigid graphs in the plane) are
Structural_rigidity
Canadian geometer (1907–2003)
an author of 12 books, including The Fifty-Nine Icosahedra (1938) and Regular Polytopes (1947). Many concepts in geometry and group theory are named
Harold Scott MacDonald Coxeter
Harold_Scott_MacDonald_Coxeter
Academic subfield of computer science
computational models are useful for special, restricted applications. Regular expressions, for example, specify string patterns in many contexts, from
Theory_of_computation
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
Representation of symmetric groups
Specht module may be found in Section 1 of "Specht Polytopes and Specht Matroids". The dimension of the Specht module V λ {\displaystyle V_{\lambda }} is
Specht_module
into the Matroid and mechas' colliding attacks, which causes a time warp that sends Alata and Bakutofuji-ER back in time and shrinks the Matroid. They eventually
List of Tensou Sentai Goseiger characters
List_of_Tensou_Sentai_Goseiger_characters
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
analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal
Lists_of_mathematics_topics
Graph of n vertices with a perfect matching for every subgraph of n-1 vertices
contracted to make a given graph G factor-critical form the bases of a matroid, a fact that implies that a greedy algorithm may be used to find the minimum
Factor-critical_graph
Set whose pairs have minima and maxima
algebras, Boolean algebras, distributive lattices, and geometric lattices (matroids). These lattice-like structures all admit order-theoretic as well as algebraic
Lattice_(order)
Branch of mathematics
be polynomial (or regular) does not depend on the choice of a coordinate system in An. When a coordinate system is chosen, the regular functions on the
Algebraic_geometry
Vertices connected in pairs by edges
they allow for higher-dimensional simplices. Every graph gives rise to a matroid. In model theory, a graph is just a structure. But in that case, there
Graph_(discrete_mathematics)
Abstract strategy board game
mathematical underpinnings related to the Brouwer fixed-point theorem, matroids and graph connectivity. Hex is a finite, two-player perfect information
Hex_(board_game)
the graphic matroid of a graph, a subset of edges is independent if the corresponding subgraph is a tree or forest. In the bicircular matroid, a subset
Glossary_of_graph_theory
Field of knowledge
Coding theory, including error correcting codes and a part of cryptography Matroid theory Discrete geometry Discrete probability distributions Game theory
Mathematics
Branch of elementary mathematics
individual operations are needed rather than the 64 operations required for regular repeated multiplication. Methods to calculate logarithms include the Taylor
Arithmetic
Branch of mathematics
as the science of geometry itself. Symmetric shapes such as the circle, regular polygons and platonic solids held deep significance for many ancient philosophers
Geometry
Branch of mathematics
addition, and has an identity element. In addition, he had two axioms on "regular elements" inspired by work on the p-adic numbers, which excluded now-common
Abstract_algebra
Vertices whose removal breaks all cycles
polynomial time, by transforming it into an instance of the matroid parity problem for linear matroids. The special case of finding all feedback vertices in
Feedback_vertex_set
Assignment of colors to edges of a graph
Westermann, Herbert H. (1992), "Forests, frames, and games: algorithms for matroid sums and applications", Algorithmica, 7 (5–6): 465–497, doi:10.1007/BF01758774
Edge_coloring
Toroidal polyhedron with 14 triangle faces
Bokowski, J.; Guedes de Oliveira, A. (2000), "On the Generation of Oriented Matroids", Discrete & Computational Geometry, 24: 197–208, doi:10.1007/s004540010027
Császár_polyhedron
1961. Elsevier. ISBN 9781483223568. Kazuo Murota (2009). Matrices and Matroids for Systems Analysis. Springer Science & Business Media. p. 47. ISBN 9783642039942
Flow_graph_(mathematics)
Convex hull of a finite set of points in a Euclidean space
a bit-length which is not polynomial in this representation. Oriented matroid Nef polyhedron Steinitz's theorem for convex polyhedra Branko Grünbaum
Convex_polytope
Measurement of graph sparsity
Westermann, H. H. (1992), "Forests, frames, and games: algorithms for matroid sums and applications", Algorithmica, 7 (1): 465–497, doi:10.1007/BF01758774
Degeneracy_(graph_theory)
Combinitorics of Polyhedra
facets are available. Abstract polytope Combinatorial commutative algebra Matroid polytope Order polytope Simplicial sphere Stable matching polytope Ziegler
Polyhedral_combinatorics
Operation in graph theory
the pivot-minor relation are essentially equivalent to binary matroids with the matroid minor relation. For a circle graph G {\displaystyle G} , performing
Local_complementation
"Cocircuit Graphs and Efficient Orientation Reconstruction in Oriented Matroids". Eur. J. Comb. 22 (5): 587–600. doi:10.1006/eujc.2001.0481. ISSN 0195-6698
Graph_of_a_polytope
Concerned with the notion of stability in model theory
e. is prime and minimal over) a strongly minimal set, which carries a matroid structure determined by (model-theoretic) algebraic closure that gives
Stable_theory
On when a space equals the closed convex hull of its extreme points
Axiom of Choice]. Krein, Mark; Milman, David (1940), "On extreme points of regular convex sets", Studia Mathematica, 9: 133–138, doi:10.4064/sm-9-1-133-138
Krein–Milman_theorem
Generalization of graph theory
abstract simplicial complex with the augmentation property is called a matroid. Laminar: for any two hyperedges, either they are disjoint, or one is included
Hypergraph
Embedding of the circle in three dimensional Euclidean space
125–136. Ramirez Alfonsin, J. L. (1999), "Spatial graphs and oriented matroids: the trefoil", Discrete and Computational Geometry, 22 (1): 149–158, doi:10
Knot_(mathematics)
American mathematician
algebraic combinatorics, including work on cell complexes associated with matroids and on chip-firing games. She is an associate professor of applied mathematics
Caroline_Klivans
Convex polyhedron projected from hypercube
prism over a regular polygon with an even number of sides forms a zonohedron. These prisms can be formed so that all faces are regular: two opposite
Zonohedron
Smallest convex set containing a given set
convex hulls may also be generalized in a more abstract way, to oriented matroids. It is not obvious that the first definition makes sense: why should there
Convex_hull
Embedding a graph in 3D space with no cycles interlinked
D. thesis, University of California, Berkeley. Truemper, Klaus (1992), Matroid Decomposition (PDF), Academic Press, pp. 100–101, archived from the original
Linkless_embedding
For example, 1.2E3 is 1.2×103 or 1200 the set of edges in a graph or matroid the unit prefix exa (1018) energy in physics electric field denoted E {\displaystyle
Latin letters used in mathematics, science, and engineering
Latin_letters_used_in_mathematics,_science,_and_engineering
affine Gale diagrams can also be described through the duality of oriented matroids. As with the linear diagram, a subset of vertices forms a face if and only
Gale_diagram
Subgraph with contracted edges
graph H. Graph minors are often studied in the more general context of matroid minors. In this context, it is common to assume that all graphs are connected
Graph_minor
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
1112/blms/18.6.571, MR 0859948 Ramírez Alfonsín, J. L. (2001), "Lawrence oriented matroids and a problem of McMullen on projective equivalences of polytopes", European
McMullen_problem
Basic concepts of algebra
is equivalent to x 1 n {\displaystyle x^{\frac {1}{n}}} . Combined with regular exponents (powers), then x 3 2 {\displaystyle {\sqrt[{2}]{x^{3}}}} (the
Elementary_algebra
Type of graph in graph theory
"Exponentially many hypohamiltonian graphs", Graphs, Hypergraphs and Matroids III (Proc. Conf. Kalsk 1988), Zielona Góra: Higher College of Engineering
Hypohamiltonian_graph
British mathematician
Springer-Verlag, p. 659, ISBN 3-540-44389-4, MR 1956925 Welsh, D. J. A. (1976), Matroid theory, London and New York: Academic Press, p. 219, ISBN 9780486474397
Hazel_Perfect
satisfying the second condition form the independent sets of a sparsity matroid, and are called ( 2 , 3 ) {\displaystyle (2,3)} -sparse. A graph satisfying
Geiringer–Laman_theorem
Number that is the product of factorials
S2CID 121878844 Golumbic, Martin Charles (1977), "Comparability graphs and a new matroid", Journal of Combinatorial Theory, Series B, 22 (1): 68–90, doi:10
Jordan–Pólya_number
the LYM inequality) Lucas chain MacMahon's master theorem Magic square Matroid embedding Monge array Monomial order Moreau's necklace-counting function
Index of combinatorics articles
Index_of_combinatorics_articles
REGULAR MATROID
REGULAR MATROID
Surname or Lastname
English
English : nickname probably for a tenant whose feudal obligations included a regular payment in cash or kind (for example bread or salt) of a halfpenny.
Boy/Male
Gujarati, Haryanvi, Hindu, Indian, Kannada, Marathi, Telugu
Regular; Ethical; Good in Nature
Male
Scandinavian
Scandinavian form of German Reginar, RAGNAR means "wise warrior."
Surname or Lastname
English, of Welsh origin
English, of Welsh origin : variant of Bevan, with the addition of the regular English patronymic suffix -s.
Girl/Female
Hebrew
Precious.
Boy/Male
Indian, Sanskrit
Connector; Regulator
Girl/Female
Arabic, Muslim
Pilgrimage to Makkah Other than Regular Hajj Days
Boy/Male
Shakespearean
King Henry IV, Part 1 and 2' An irregular humorist.
Girl/Female
Indian
One who remembers Allah regularly
Boy/Male
Hindu, Indian, Traditional
Conduct; Regular Performance of Worship
Surname or Lastname
North German
North German : variant of Asch.English : variant spelling of Ash (asche was the regular Middle English spelling of this word).
Male
Spanish
Spanish form of Roman Latin Regulus, RÉGULO means "ruler."
Boy/Male
Hindu, Indian, Tamil
Regular Winner
Male
German
A derivative of German Reginar, RAINER means "wise warrior."
Girl/Female
Muslim
One who remembers Allah regularly
Male
Italian
Italian form of German Reginar, RANIERO means "wise warrior."
Girl/Female
Muslim/Islamic
One who remembers Allah regularly
Surname or Lastname
English (Devon)
English (Devon) : unexplained. Possibly an irregular variant of Birchall.
Boy/Male
Shakespearean
King Henry IV, Part 1 and 2' Edward Poins, an irregular humorist.
Surname or Lastname
English, of Welsh origin
English, of Welsh origin : variant of Bowen, with the addition of the regular English patronymic suffix -s.Altered spelling of Dutch Bouwens, a variant of Bauwens.
REGULAR MATROID
REGULAR MATROID
Girl/Female
Arabic, Muslim
Publisher; Spreader
Boy/Male
Spanish American
Young lion.
Boy/Male
Tamil
Flute
Girl/Female
Norse
Fiery spirit.
Boy/Male
Tamil
It is one of the Lord Vishnu name
Surname or Lastname
English
English : topographic name for someone who lived at the foot of a hill, or a habitational name from Underhill in Devon, named from Old English under ‘under’ + hyll, or from Underhill in Kent, named from Old English under + helde ‘slope’.John Underhill (c.1597–1672) was born in Kenilworth, Warwickshire, England. His father was a mercenary in the Netherlands, and he himself became a cadet in the Prince of Orange’s guards. In 1630 he emigrated to Boston, MA, where he was appointed captain of militia. In 1664–65 he played a significant role in helping to bring the Dutch colony of New Netherland under English control.
Boy/Male
Bengali, Hindu, Indian, Kannada, Marathi, Telugu
Related
Boy/Male
Biblical
Men of anger; or of fury; or of liberty.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Pledge; Vow
Boy/Male
Muslim
Glory
REGULAR MATROID
REGULAR MATROID
REGULAR MATROID
REGULAR MATROID
REGULAR MATROID
a.
Belonging to a monastic order or community; as, regular clergy, in distinction dfrom the secular clergy.
pl.
of Regulus
n.
One who is not regular; especially, a soldier not in regular service.
a.
Not regular; not bound by monastic vows or rules; not confined to a monastery, or subject to the rules of a religious community; as, a secular priest.
a.
Constituted, selected, or conducted in conformity with established usages, rules, or discipline; duly authorized; permanently organized; as, a regular meeting; a regular physican; a regular nomination; regular troops.
a.
Having all the parts of the same kind alike in size and shape; as, a regular flower; a regular sea urchin.
a.
Conformed to a rule; agreeable to an established rule, law, principle, or type, or to established customary forms; normal; symmetrical; as, a regular verse in poetry; a regular piece of music; a regular verb; regular practice of law or medicine; a regular building.
adv.
In a regular manner; in uniform order; methodically; in due order or time.
pl.
of Tegula
v. t.
To cause to become regular; to regulate.
n.
A secular ecclesiastic, or one not bound by monastic rules.
a.
Irregular in position; having no regular order; as, scattered leaves.
a.
Fig.: Lean; lank; raw-boned; ungraceful; sharp and stiff in character; as, remarkably angular in his habits and appearance; an angular female.
a.
Thorough; complete; unmitigated; as, a regular humbug.
a.
Of or pertaining to a tile; resembling a tile, or arranged like tiles; consisting of tiles; as, a tegular pavement.
a.
Measured by an angle; as, angular distance.
a.
Governed by rule or rules; steady or uniform in course, practice, or occurence; not subject to unexplained or irrational variation; returning at stated intervals; steadily pursued; orderlly; methodical; as, the regular succession of day and night; regular habits.
a.
Of or pertaining to the jugular vein; as, the jugular foramen.
n. pl.
A division of Echini which includes the circular, or regular, sea urchins.
a.
Not regular; not conforming to a law, method, or usage recognized as the general rule; not according to common form; not conformable to nature, to the rules of moral rectitude, or to established principles; not normal; unnatural; immethodical; unsymmetrical; erratic; no straight; not uniform; as, an irregular line; an irregular figure; an irregular verse; an irregular physician; an irregular proceeding; irregular motion; irregular conduct, etc. Cf. Regular.