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	Matroid - Wikipedia, the free encyclopedia
		In combinatorial mathematics, a matroid is a structure that captures the essence of a notion of "independence" (hence independence structure) that generalizes linear independence in vector spaces.
		In the linear algebra example matroid above, a basis is a basis in the sense of linear algebra of the subspace spanned by E, and a circuit is a minimal set of dependent vectors of E.
		In the cycle matroid, a basis is the same as a spanning forest of the graph G, and circuits are simple cycles in the graph.
	en.wikipedia.org /wiki/Matroid (2621 words)

	PlanetMath: matroid
		A matroid is a combinatorial structure whose properties imitate those of linearly independent subsets of a vector space.
		This notion of duality agrees with the notion of same name in the theory of planar graphs (and likewise in linear algebra): given a plane graph, the dual of its matroid is the matroid of the dual graph.
		The dual of a binary matroid is binary.
	planetmath.org /encyclopedia/Matroid.html (1032 words)

	Matroid Theory (Site not responding. Last check: 2007-11-03)
		The matroid of a graph and graph planarity.
		The matroid of circuits of a graph, circuit isomorphisms and semi-isomorphisms of graphs.
		Geometrical and matroid dualities of graphs, a planarity criterion of a graph in terms of its matroid.
	www.cnnet.clu.edu /math/profs/pennance/courses/8041.php (441 words)

	Matroid Theory
		Matroids are an abstraction of several combinatorial objects, among them graphs and matrices.
		The word matroid was coined by Whitney in 1935 in his landmark paper "On the abstract properties of linear dependence".
		Matroid theory provides a framework in which problems in combinatorial optimization, operations research and graph theory become simpler to understand.
	members.aol.com /matroids (341 words)

	Matroid embedding - Wikipedia, the free encyclopedia
		In combinatorics, a matroid embedding is a set system (F, E), where F is a collection of feasible sets, that satisfies the following properties:
		The collection of all subsets of every feasible set forms a matroid.
		Matroid embedding was introduced by Helman et al.
	en.wikipedia.org /wiki/Matroid_embedding (199 words)

	[No title]
		Such oriented matroids can be given a partial ord* *er by using the notion of weak maps, which geometrically corresponds to moving the k-plane into more special position with respect to the standard basis of Rn.
		As far as geometric topology is concerned, a matroid bundle over a finite cell complex is a purely finite gadget, and we have shown that matroid bundles have characteristic class information.
		Definition 2.2.The universal rank k matroid bundle is flk = (MacP (k; 1); Id) Definition 2.3.A rank k combinatorial vector bundle = (B; M) is a piecewise-linear (PL) cell complex B and a poset map M from the set of cells of a PL subdivision of B, ordered by inclusion, to MacP (k; 1).
	hopf.math.purdue.edu /Anderson-DavisJ/MacPherson.txt (10614 words)

	Home Page of Joseph E. Bonin
		Matroid theory began in the 1930's as an abstraction of the ideas of linear independence in linear algebra, algebraic independence in field theory, and cycle-free edge sets in graph theory.
		The 1960's and 70's witnessed an explosive growth in the field, spurred partly by the discovery of connections with optimization: for instance, matroids are the simplicial complexes on which the greedy algorithm produces optimal solutions, and they are the combinatorial structure behind linear programming.
		Bonin and A. de Mier, The lattice of cyclic flats of a matroid.
	home.gwu.edu /~jbonin (882 words)

	Oriented Matroid Theory
		The framework of oriented matroids is by now a well-developed tool to study various kinds of combinatorial problems.
		The latter example is the oriented matroid of the vector configuration of homogenous coordinates of the vertices of the standard cyclic polytope
		Figure 1.9 shows a zonotopal tiling corresponding to the non-realizable oriented matroid given by the so-called ``non-Pappus'' pseudoline configuration.
	www.uni-bayreuth.de /departments/wirtschaftsmathematik/rambau/Diss/diss_MASTER/node14.html (455 words)

	VEGA 0.5 Quick Reference Manual: Functions in MATROID.M
		CycleIndependQ[Cyc, X] returns True X is an independent set in a matroid with a family of cycles Cyc and False otherwise.
		FindJ[S, C] returns a family of an independent sets of matroid with underlying set S and family of cycles C. FindJ[S, r] returns a family of an independent sets of matroid with underlying set S and range function r.
		Matroid[S, J] is a matroid with an underlying set S and a family of independent sets J. Matroid[n, J] is a matroid with underlying set Range[n] and independent family J. MatroidOneSum
	vega.ijp.si /Htmldoc/usages/MATROID.HTM (944 words)

	Some Problems in Matroid Theory (Site not responding. Last check: 2007-11-03)
		Given a matroid and a number r, you want to find the size of a largest flat with rank r.
		Kahn and Kung say a matroid "splits" if it is the disjoint union of two proper flats.
		The flat packing number p(M) of a matroid M is the smallest number of proper flats (that is, we may use any flat except the whole point set) that are pairwise disjoint and whose union is the whole point set.
	www.math.binghamton.edu /zaslav/Matroids/matroidprobs.html (488 words)

	The Home Page of James Oxley
		Here is an introduction to matroid theory entitled "What is a matroid?", in Postscript format and in pdf format.
		It was prepared for presentation at the Workshop on Combinatorics and its Applications run by the New Zealand Institute of Mathematics and its Applications in Auckland in July, 2004.
		The structure of a 3-connected matroid with a 3-separating set of essential elements, Discrete Math.
	www.math.lsu.edu /~oxley (656 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		3 in binary @comment "the matroid ND11 - excluded for bw.
		3 in binary" 1 0 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 0 @require 1+1 0 }{ # # the matroid ND11 - excluded for bw.
		3 in binary" }{ # # the matroid ND23 - excluded for bw.
	www.mcs.vuw.ac.nz /research/macek/bw3/files/bw3-bin-exc (130 words)

	Coxeter Matroid Polytopes - Borovik, Gelfand, White (ResearchIndex)
		The exchange group W (\Delta) is the group generated by these reflections, and \Delta is a (Coxeter) matroid polytope if this group is finite.
		This simple concept of matroid polytope turns out to be an equivalent way to define Coxeter matroids.
		Borovik, I. Gelfand and N. White, Coxeter matroid polytopes, Annals of Combinatorics, 1 (1997) 123-134.
	citeseer.ist.psu.edu /293951.html (501 words)

	Las Vergnas: The Tutte polynomial of a morphism of matroids I. Set-pointed matroids and matroid perspectives
		The Tutte polynomial of a morphism of matroids I. Set-pointed matroids and matroid perspectives.
		We study the basic algebraic properties of a 3-variable Tutte polynomial the author has associated with a morphism of matroids, more precisely with a matroid strong map, or matroid perspective in the present paper, or, equivalently by the Factorization Theorem, with a matroid together with a distinguished subset of elements.
		two-variable Tutte polynomials of the matroids of its Higgs factorization.
	www.numdam.org /numdam-bin/item?id=AIF_1999__49_3_973_0 (516 words)

	Is each Mader matroid a gammoid? (ResearchIndex)
		A matroid is a gammoid if and only if it is a contraction of a Menger matroid.
		7 Gammoids and transversal matroids (context) - Ingleton, Piff - 1973
		2 the vector representation of matroids (context) - Piff, Welsh - 1970
	citeseer.ist.psu.edu /464536.html (296 words)

	Amazon.com: Matroid Theory (Oxford Graduate Texts in Mathematics): Books: James G. Oxley (Site not responding. Last check: 2007-11-03)
		The study of matroids is a branch of discrete mathematics with basic links to graphs, lattices, codes, transversals, and projective geometries.
		Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical engineering and statics.
		incisive survey of matroid theory falls into two parts: the first part provides a comprehensive introduction to the basics of matroid theory while the second treats more advanced topics.
	www.amazon.com /exec/obidos/tg/detail/-/0198535635?v=glance (672 words)

	A.V.Borovik. Matroid maps...
		The maximality property in this case is nothing else but the well-known optimal property of matroids first discovered by Gale [3].
		Its existence, under the assumption that the parabolic subgroup P is finite, is shown in [2, Lemma 5.14].
		If is a matroid map then the satisfaction of conditions (1) and (2) is the main result of [2].
	www.omsu.omskreg.ru /vestnik/articles/y1997-i1/a012/article.html (752 words)

	ECCC Report TR05-016 and related Papers (Site not responding. Last check: 2007-11-03)
		We generalize this result to delta-matroids that do not have equality as a restriction, and give a polynomial time algorithm for delta-matroid intersection on delta-matroids without equality using an oracle.
		We also obtain algorithms using an oracle for delta-matroid parity on delta-matroids without inequality, and for delta-matroid intersection where one delta-matroid does not contain either equality or inequality, and the second delta-matroid is arbitrary.
		The results imply a dichotomy for bipartite Boolean constraint satisfaction problems using an oracle when one of the two sides does not contain equality, leaving open cases of delta-matroid parity when both sides have equality; the results also imply a full dichotomy for $k$-partite Boolean constraint satisfaction problems for $kgeq 3$.
	www.eccc.uni-trier.de /eccc-reports/2005/TR05-016 (247 words)

	Matroid Miscellany (Site not responding. Last check: 2007-11-03)
		An overview of many of the multiplicity of "cryptomorphisms" (equivalent but seemingly wildly different ways to define matroids); an antidote to the "Let (E, X) be a matroid" style of pseudo-definition.
		Joseph P.S. Kung, "Extremal matroid theory", in: Neil Robertson and Paul Seymour, eds.,
		Anders Björner, "Homology and shellability of matroids and geometric lattices", Ch.
	www.math.binghamton.edu /zaslav/Matroids (248 words)

	CiteULike: Tag matroid (Site not responding. Last check: 2007-11-03)
		A common recursion for Laplacians of matroids and shifted simplicial complexes
		The Bergman complex of a matroid and phylogenetic trees
		The Positive Bergman Complex of an Oriented Matroid
	www.citeulike.org /tag/matroid (77 words)

	Truemper: Matroid Decomposition (Site not responding. Last check: 2007-11-03)
		Abstract: Matroids were first defined in 1935 as an abstract generalization of graphs and matrices.
		As this book is being written, a large collection of deep matroid theorems already exists.
		Permission is granted to inviduals to print single copies of the book for personal use without charge by the publisher.
	www.emis.de /monographs/md (218 words)

	Works Citing the On-Line Encyclopedia of Integer Sequences (Site not responding. Last check: 2007-11-03)
		Bonin, A. de Mier, and M. Noy, Lattice path matroids: enumerative aspects and Tutte polynomials, Journal of Combinatorial Theory, Series A, to appear.
		Duchon, P. Flajolet, G. Louchard and G. Schaeffer, Boltzmann Samplers for the Random Generation of Combinatorial Structures, Submitted to Combinatorics, Probablity, and Computing, Special issue on Analysis of Algorithms, January 2003.
		On a Unimodality Conjecture in Matroid Theory, Discrete Math.
	www.research.att.com /~njas/sequences/cite.html (8938 words)

	SIDMA Volume 17 Issue 2 (Site not responding. Last check: 2007-11-03)
		We consider a problem of maximizing convex functionals over matroid bases.
		While generally intractable, we show that it is efficiently solvable when a suitable parameter is restricted.
		combinatorial optimization, polynomial time, strongly polynomial time, convex, optimization, partition, cluster, matroid, greedy algorithm, quadratic assignment, polytope
	epubs.siam.org /sam-bin/dbq/article/40855 (140 words)

	Encyclopaedia of Design Theory: Bibliography
		Peter J. Cameron, Finite geometry and coding theory
		Peter J. Cameron, Polynomial aspects of codes, matroids and permutation groups
		(A) M.~Deza, Perfect matroid designs, Encyclopedia of Mathematics and its Applications 40 (1992), 54-72.
	www.designtheory.org /library/encyc/biblio (1646 words)

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