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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
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
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 in which every permutation is a symmetry
In mathematics, a uniform matroid is a matroid in which the independent sets are exactly the sets containing at most r elements, for some fixed integer
Uniform_matroid
Independence system partitionable into circuits
In matroid theory, an Eulerian matroid is a matroid whose elements can be partitioned into a collection of disjoint circuits. In a uniform matroid U n
Eulerian_matroid
Abstraction of 2-colorable graphs
duality extends to binary matroids: a binary matroid is bipartite if and only if its dual matroid is an Eulerian matroid, a matroid that can be partitioned
Bipartite_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
Matroid with complemented basis sets
generally among the binary matroids, the bipartite matroids (matroids in which every circuit is even) are dual to the Eulerian matroids (matroids that can be
Dual_matroid
Graph representing faces of another graph
to binary matroids (which include the graphic matroids derived from planar graphs): a binary matroid is Eulerian if and only if its dual matroid is bipartite
Dual_graph
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
Abstraction of graph shortest cycles
In matroid theory, a mathematical discipline, the girth of a matroid is the size of its smallest circuit or dependent set. The cogirth of a matroid is
Matroid_girth
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
British-Canadian codebreaker and mathematician (1917–2002)
regular matroids, about which he proved deep results. In addition, Tutte developed an algorithm for determining whether a given binary matroid is a graphic
W._T._Tutte
Maximum size of an independent set of the matroid
theory of matroids, the rank of a matroid is the maximum size of an independent set in the matroid. The rank of a subset S of elements of the matroid is, similarly
Matroid_rank
Conjecture on forbidden minors of matroids
proved that the binary matroids (matroids representable over the field of two elements) have a single forbidden minor, the uniform matroid U 4 2 {\displaystyle
Rota's_conjecture
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
Operation on the subsets of a set
of a relation is the smallest equivalence relation that contains it. In matroid theory, the closure of X is the largest superset of X that has the same
Closure_(mathematics)
Abstract strategy board game
mathematician Alfred Lehman showed that Hex cannot be represented as a binary matroid, so a determinate winning strategy like that for the Shannon switching
Hex_(board_game)
Hierarchical clustering of graph edges
Branch-decompositions and branchwidth may also be generalized from graphs to matroids. An unrooted binary tree is a connected undirected graph with no cycles in which
Branch-decomposition
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
Operation in graph theory
with 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
sets of a matroid. For example, every bundle must contain at most k items, where k is a fixed integer (this corresponds to a uniform matroid). Or, the
Welfare_maximization
Geometry with 7 points and 7 lines
structure theory of matroids. Excluding the Fano plane as a matroid minor is necessary to characterize several important classes of matroids, such as regular
Fano_plane
Method to solve optimization problems
Method of computing optimal strategies for last-success problems Oriented matroid – Abstraction of ordered linear algebra Quadratic programming – Solving
Linear_programming
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
Graph cycle which does not separate remaining elements
a two-edge path) but the graphic matroid formed by this bridge is not connected, so no circuit of the graphic matroid of K 2 , 3 {\displaystyle K_{2,3}}
Peripheral_cycle
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)
Set-to-real map with diminishing returns
vector. Matroid rank functions Let Ω = { e 1 , e 2 , … , e n } {\displaystyle \Omega =\{e_{1},e_{2},\dots ,e_{n}\}} be the ground set on which a matroid is
Submodular_set_function
American mathematician
is important in matroid theory. In that 1966 paper, according to Dominic Welsh: The circuit space and cocircuit space of binary matroids were introduced
George_J._Minty
Branch of mathematics
branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such
Order_theory
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)
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)
American mathematician
University. Her dissertation, Minors of 3-Connected Matroids and Adjoints of Binary Matroids, concerned matroid theory and was supervised by Robert E. Bixby
Collette_Coullard
Abstract machine used to study decision problems
random oracle). Black box group Turing reduction Interactive proof system Matroid oracle Demand oracle Padding oracle attack van Melkebeek 2003, Section
Oracle_machine
Branch of mathematics
identity 1, today called a monoid. In 1870 Kronecker defined an abstract binary operation that was closed, commutative, associative, and had the left cancellation
Abstract_algebra
Social choice problem
Munagala and Shah focus on three types of constraints: Matroid constraints: there is a fixed matroid M over the items, and the chosen items must form a basis
Multi-issue_voting
Relation showing how elements rely on each other
dependence relation is a binary relation which generalizes the relation of linear dependence. Let X {\displaystyle X} be a set. A (binary) relation ◃ {\displaystyle
Dependence_relation
Any collection of sets, or subsets of a set
of a set in F {\displaystyle F} is also in F {\displaystyle F} . A matroid is an abstract simplicial complex with an additional property called the
Family_of_sets
Branch of elementary mathematics
the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers
Arithmetic
Ternary relation on points in the plane
correspondence between CC systems and uniform acyclic oriented matroids of rank 3. These matroids in turn have a 1-1 correspondence to topological equivalence
CC_system
Concept from mathematical logic
an infinite matroid, or pregeometry. A model of a strongly minimal theory is determined up to isomorphism by its dimension as a matroid. Totally categorical
Strongly_minimal_theory
Mathematical operator
A and {x}. A finitary closure operator with this property is called a matroid. The dimension of a vector space, or the transcendence degree of a field
Closure_operator
Natural number
its original position horizontally, vertically, or diagonally, and 185 matroids on five labeled elements in which each element participates in at least
185_(number)
Mathematical ordering of a partial order
Günter M. (1992), "Introduction to Greedoids", in White, Neil (ed.), Matroid Applications, Encyclopedia of Mathematics and its Applications, vol. 40
Linear_extension
Relation on disjoint pairs of sets
framework of separoids; e.g., graphs, configurations of convex sets, oriented matroids, and polytopes. Any countable category is an induced subcategory of separoids
Separoid
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
of it include enumerative combinatorics, combinatorial design theory, matroid theory, extremal combinatorics and algebraic combinatorics, as well as
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Algorithm that outputs all solutions to a problem
the Bron–Kerbosch algorithm Listing all elements of structures such as matroids and greedoids Several problems on graphs, e.g., enumerating independent
Enumeration_algorithm
Economical computational problem
the bases of a matroid over the set of resources, then all best-response sequences converge in polynomial number of steps, and the matroid property is essential
Nash_equilibrium_computation
and using the Biswas-Barman algorithm for fair allocation with partition matroid constraints, or simply by round-robin item allocation. This guarantees
Temporal_fair_division
Combinitorics of Polyhedra
facets are available. Abstract polytope Combinatorial commutative algebra Matroid polytope Order polytope Simplicial sphere Stable matching polytope Ziegler
Polyhedral_combinatorics
Elad; Carmesin, Johannes; Fröhlich, Jan-Oliver (2012-07-09), Infinite matroid union, arXiv:1111.0602 Blossier, Thomas; Bouscaren, Elisabeth (2010). "Finitely
Glossary_of_logic
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
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
Fair item allocation problem
item. 3. When all agents have valuations that are matroid rank functions (i.e., submodular with binary marginals), the set of absolute-leximin allocations
Egalitarian_item_allocation
Computer Networking Program
3247570. S2CID 248986512. Kühne, L.; Yashfe, G. (2022). "Representability of Matroids by c-Arrangements is Undecidable". Israel Journal of Mathematics. 252:
Linear_network_coding
American mathematician
(2012), no. 4, 911–922. 2013 Branch decomposition heuristics for linear matroids Archived October 15, 2018, at the Wayback Machine (with Jing Ma, Susan
Edray_Herber_Goins
Algorithmically defined graph
group, an implicit model for group-theoretic algorithms Matroid oracle, an implicit model for matroid algorithms Korf, Richard E. (2008), "Linear-time disk-based
Implicit_graph
Computational problem in graph theory
ISSN 0022-0000. Eugene Lawler (2001). "4. Network Flows". Combinatorial Optimization: Networks and Matroids. Dover. pp. 109–177. ISBN 978-0-486-41453-9.
Maximum_flow_problem
requirement that the union of all allocated goods is a basis of a given matroid. They used an algorithm similar to the envy-graph procedure. Suksompong
Efficient approximately fair item allocation
Efficient_approximately_fair_item_allocation
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)
mathematician specializing in disease modeling Collette Coullard, American matroid theorist and operations researcher Judith Covington, American mathematics
List_of_women_in_mathematics
Fair division problem for discrete items
variant is known as the agreeable subset problem. There may be general matroid constraints, matching constraints or knapsack constraints on the chosen
Fair_item_allocation
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
gender-affirmation and other social determinants shape the health of transgender and non-binary people. Indigenous politics and civic participation. Associate Professor
Rutherford Discovery Fellowships
Rutherford_Discovery_Fellowships
Criterion of fair item allocation
guarantee, that works for the more general problem of allocating a basis of a matroid. Li, Moulin, Sun and Zhou have extended Hill's lower bound to bads, and
Maximin_share
Basic concepts of algebra
most common case is the case of arity two, where the operation is called a binary operation and the operands form an ordered pair. A unary operation is an
Elementary_algebra
BINARY MATROID
BINARY MATROID
Male
Hindi/Indian
Variant spelling of Hindi Vijay, BIJAY means "victory."
Male
Hindi/Indian
(विनय) Hindi name VINAY means "leading asunder."
Girl/Female
Indian
(the wife of Sage Kashyap)
Female
Hebrew
Variant spelling of Hebrew Bina, BINAH means "intelligence, wisdom."Â
Female
Turkish
Turkish name PINAR means "spring."
Female
Hebrew
(×‘Ö¼Ö´×™× Ö¸×”) Hebrew name BINA means "intelligence, wisdom."Â
Girl/Female
Hindu
Shore, Musical instrument, Goddess of wealth
Girl/Female
Indian
Modesty
Surname or Lastname
English
English : variant spelling of Vickery.
Boy/Male
American, Australian, French, German, Greek, Latin, Polish, Swedish
Cheerful; Happy; Joyful; Similar to Hilary
Male
English
English unisex form of Latin Hilarius and Hilaria, HILARY means "joyful; happy."Â Originally, this was strictly a masculine name.
Surname or Lastname
English (chiefly South Yorkshire)
English (chiefly South Yorkshire) : topographic name for someone who lived on land enclosed by a bend in a river, from Old English binnan ēa ‘within the river’, or a habitational name from places in Kent called Binney and Binny, which have this origin.Scottish : habitational name from Binney or Binniehill near Falkirk, named in Gaelic as Beinnach, from beinn ‘hill’ + the locative suffix -ach.
Boy/Male
Irish
An ancient Irish name whos meaning is lost in antiquety.
Girl/Female
Hindu
Shore, Musical instrument, Goddess of wealth
Boy/Male
Indian
An intimate particle of the God of heaven
Male
Scandinavian
Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."
Boy/Male
Indian, Punjabi, Sikh
Blessing
Girl/Female
English
Originally a diminutive used for names ending in -bina, like Albina, Columbina, and Robina, now...
Female
English
English pet form of German Belinda, possibly BINDY means "bright serpent" or "bright linden tree."
Boy/Male
Latin
Happy; Cheerful.
BINARY MATROID
BINARY MATROID
Girl/Female
Greek American Teutonic Latin
Well spoken.
Female
English
Feminine form of Irish Brian, BRENNA means "high hill."
Girl/Female
Indian, Telugu, Traditional
Brave
Girl/Female
Indian
Abbreviation of elisabeth
Boy/Male
Gujarati, Hindu, Indian, Modern
To Rise
Girl/Female
Indian, Punjabi, Sikh
Time
Girl/Female
Hebrew Biblical
God's glory.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Beautiful
Boy/Male
Indian, Punjabi, Sikh
Warrior of the World
Girl/Female
American, British, Christian, English, Hebrew
God is Gracious; God will Add; Gift of God
BINARY MATROID
BINARY MATROID
BINARY MATROID
BINARY MATROID
BINARY MATROID
n.
That which is constituted of two figures, things, or parts; two; duality.
n.
A binary compound of silicon, or one regarded as binary.
a.
Of or pertaining to the Canary Islands; as, canary wine; canary birds.
n.
A binary compound of zinc.
a.
Of a pale yellowish color; as, Canary stone.
n.
A register of daily events or transactions; a daily record; a journal; a blank book dated for the record of daily memoranda; as, a diary of the weather; a physician's diary.
n.
Wine made in the Canary Islands; sack.
n.
A binary compound of hydrogen; a hydride.
n.
A binary compound of iodine, or one which may be regarded as binary; as, potassium iodide.
a.
Containing ten; tenfold; proceeding by tens; as, the denary, or decimal, scale.
a.
Relating or belonging to bile; conveying bile; as, biliary acids; biliary ducts.
n.
A binary compound of phosphorus.
a.
Compounded or consisting of two things or parts; characterized by two (things).
a.
lasting for one day; as, a diary fever.
a.
Of or pertaining to the urine; as, the urinary bladder; urinary excretions.
n.
A pale yellow color, like that of a canary bird.
n.
A canary bird.
n.
See Finery.
n.
A binary compound of selenium, or a compound regarded as binary; as, ethyl selenide.
v. i.
To perform the canary dance; to move nimbly; to caper.