Found inside – Page 4577... models) underlying matroid [90009, 90010] (see: Oriented matroids) underlying method ... resource constrained: — uniform [49M37, 65K10, 901336, 90626, ... Found inside – Page 113Triangle sign encodings of arrangements are related to chirotopes of uniform rank 3 oriented matroids (see (28). A result similar to Theorem 6.17 was ... Found inside – Page 187The oriented matroid is uniform when all hyperline sequences are uniform. Theorem 1. The hyperline sequences HS(PLn) of an oriented pseudoline arrangement ... Found inside – Page 363(182) Neil White: A non-uniform oriented matroid which violates the isotopy property, Discrete Comput. Geometry 4 (1989), 1-2. (179) John Henry Constantine ... Found inside – Page 343In the same way we construct the ((oriented) matroid) rank 2 contractions of ... Peter Schuchert) for generating recursively all uniform oriented matroids ... Found inside – Page 191(3.3) Lemma Let '6' and Ø be dual oriented matroids on a paired set I, ... (3.4) Lemma Consider the uniform matroid 4/2.4 of rank 2 on a set of four ... Found inside – Page 241Remark that the main part of computation time is needed for generating the uniform oriented matroids. This is because we need to consider the whole S7 as ... Found inside – Page 535The properties of χM are known as the uniform oriented matroid theory [2]. This rich mathematical theory is forty years old and can be seen as a ... Found inside – Page 234It is unknown whether or not one obtains additional matrices N from the "linear programming problems" derived in the setting of uniform oriented matroids. Found inside – Page 92By applying oriented matroid theory (see the next subsection) Naimi and Pavelescu ... Rather we give enough of a partial definition of a uniform oriented ... Found inside – Page 256oriented. matroid. level. From [8] we know that certain triangulated ... with the oriented matroid condition when there is a uniform acyclic oriented ... Found inside – Page 139Moreover, it applies to plane projections of spatial graphs encoded by rank 4 uniform oriented matroids. Keywords: Graph drawing, logical structure, ... Found inside – Page 17Let M be a uniform oriented matroid so that no minor ( on at least two elements ) has an isolated element . Then M is strongly euclidean . Proof . We proceed by induction on the rank and cardinality of M. Suppose M is not strongly euclidean ... Found inside – Page 345( Bi - M1 ) Billera , L.J. & Munson , B.S. - Triangulation of Oriented Matroids and Convex Polytopes , SIAM J. on ... ( C - D ] , & Cordovil , R. & Duchet , P. - On Sign - Invariance Graphs of Uniform Oriented Matroids , Discrete Math . , to appear . Found inside – Page 1012Oriented matroids This section surveys the facts from the theory of oriented matroids we will need . It is inevitably very brief ; for ... An oriented matroid is uniform if y ( ni , . . . , nr ) = 0 for all { n1 , . . . , nr } E ( ) . An oriented matroid is acyclic if ... Found inside – Page 16These axioms form one of the several axiom systems that define uniform acyclic rank-3 oriented matroids [3]. An abstract order type χ is realizable if there ... Found inside – Page 78... K is equivalent to the readability problem for oriented matroids over K. We ... and N. White, Uniform oriented matroids without the isotopy property. Found inside – Page 153gammoids, oriented matroids, Boolean algebras, matroids with at most k points, and uniform matroids (those that are truncations of Boolean algebras). Found inside – Page 37Let M be an acyclic uniform oriented matroid of rank r on n. elements. Let all be any element. Let H M be the affine span of the characteristic vectors of ... Found insideThe book collects results about realization spaces of polytopes. Found inside – Page 581The matroid polytope we started with has 35 facets. Las Vergnas asked the following: is it possible to gain all uniform oriented matroids by just switching ... Found inside – Page 310... to be very likely because we use all non-realizable oriented matroids. ... the number of reorientations classes of uniform oriented matroids of rank 3. Found inside – Page 73Therefore Theorems 2.5.3 and 2.5.4 give the and This rank of M ' My for any pair M. , My of oriented matroids . Note that while my and M2 both free implies MoMa is uniform , M м . both uniform does not lead to MOM being uniform . is indicated ... Found inside – Page 432... to a unique isomorphism class of oriented matroids , hence every abstract ... i.e. , abstract order types corresponding to uniform oriented matroids ... Found inside – Page 237Universality. Theorem. on. the. Oriented. Matroid. Stratification ... can be represented as a realization space of a uniform, rank three oriented matroid. Found inside – Page 103Oriented matroids without the isotopy property This section gives complete proofs for the existence of oriented matroids and uniform oriented matroids ... Found inside – Page 35... Miyagi: Complete Enumerati0n of Small Realizable Oriented Matroids By a News ... database of oriented matroids including degenerate (i.e., non-uniform) ... Found inside – Page 174A similar result holds for uniform oriented matroids, that is, oriented matroids which generalize cubical zonotopes; cf. Cordovil, Fukuda, and Guedes de ... Found inside – Page 148... a uniform oriented matroid of rank 3 corresponding to each graph in this class. These oriented matroids are combinatorial representations of simple ... Found inside – Page 13of a graphic oriented oriented matroid may not be again graphic . However , if ME M ( H ) for some ... A uniform oriented matroid of rank d on E , an n - element set , is denoted by Vol , where d < n . It is an oriented matroid where every d ... We consider the concept of triangulation of an oriented matroid. Found inside – Page 205An Introduction to Oriented Matroids Achim Bachem, Walter Kern ... B. STURMFELs, N.L. WHITE, (1989), Uniform Oriented Matroids without the isotopy property, ... Found inside – Page 5839The authors characterize the cocircuit graph of a uniform oriented matroid on a finite set E by means of the existence of a certain map from the graph into the k - skeleton of the dual of the \ E \ -cube . Since the faces of the E - cube are in one - to ... Found inside – Page 833.4 Uniform chirotopes and hyperline sequences Observe that the orientation of a triangle appears three times in the hyperline sequences. Found inside – Page 822In the rank d uniform oriented matroid associated with a vector configuration in general position in Rd , all the d - tuples are bases , all the ( d + 1 ) ... Found inside – Page 328rank r uniform oriented matroid on n elements with n < 2r, then we can replace M by M* which is a rank n — r uniform oriented matroid on n Z 2(n - r) ... Found inside – Page 182Oriented k-out-of-n Systems Let (E,φ) be a binary monotone system where ... We then consider what is known as a “uniform” oriented matroid (E ∪ x,M) ... Found inside – Page 85The following table contains representatives of all 24 non-realizable reorientation classes of uniform oriented matroids in rank 4 with 8 elements, [16]. Found inside – Page 197MIe/ on an oriented matroid M is the same as the classification of the associated ... This is the case of the uniform matroids, Un;d corresponding to ... Found inside – Page 1... the authors reduced the characterization of visibility graphs of simple polygons to the coordinatization of certain uniform rank 3 oriented matroids. Found inside – Page 33We also show that the union operation is particularly simple to describe when the underlying matroids are uniform, and, equivalently, for simple oriented ... Found inside – Page 174In particular , up to change of orientations and permuting the elements in E there is only one uniform oriented matroid of rank 2. The realization space of ... Found inside – Page 114For a given (uniform) rank 3 oriented matroid with n + 1 elements, we consider its (simple) pseudoline representation with n + 1 oriented pseudolines A. Found inside – Page 217If we restrict our attention to uniform oriented matroids – they correspond to the case where points are in general position – we need only one variable; ... Found inside – Page 144In partic– ular, up to change of Orientations and permuting the elements in E there is only one uniform oriented matroid of rank 2. 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