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| contribution = Sylvester matroids ...the [[Fano plane]] and the [[Hesse configuration]] give rise to Sylvester matroids with seven and nine elements respectively, and may be interpreted either as ...

...[[semialgebraic set|semialgebraic]]) varieties as realization spaces of [[oriented matroid]]s.{{r|mnev88|vershik88}} ...Then <math>V</math> is stably equivalent to the realization space of some oriented matroid. ...

...}}, pp. 170–172.</ref> Indeed, it is one of the smallest non-representable matroids,<ref>{{harvtxt|Oxley|2006}}, Prop. 6.4.10, p. 196. A proof of representabil ...erexample to a conjecture of [[Aubrey William Ingleton|Ingleton]] that the matroids on eight or fewer elements were all representable.<ref>{{citation ...

Signed sets are fundamental to the definition of [[oriented matroid]]s.{{r|lv}} | title = Convexity in oriented matroids ...

...ute, but [[parameterized complexity|fixed-parameter tractable]] for linear matroids when parameterized both by the [[matroid rank]] and the field size of a lin The girth of other classes of matroids also corresponds to important combinatorial problems. For instance, the gir ...

...ented matroid]]s of [[matroid rank|rank]] 3.{{sfnp|Knuth|1992|p=40}} These matroids in turn have a 1-1 correspondence to topological equivalence classes of pse [[Category:Oriented matroids]] ...

[[File:max-flow min-cut example.svg|frame|right|Oriented-matroid theory allows a combinatorial approach to the [[max-flow min-cut th ...ünter M. Ziegler]], Chapter 7.</ref> In comparison, an ordinary (i.e., non-oriented) [[matroid]] abstracts the [[linear independence|dependence]] properties th ...

...|last5=Ziegler|first5=Günter|author-link5=Günter M. Ziegler|title=Oriented Matroids|chapter=10 Linear programming|publisher=Cambridge University Press|year=199 ===Oriented matroids=== ...

...e Avis–Fukuda algorithm adapted the [[criss-cross algorithm]] for oriented matroids. ...

...last4=White | first4=Neil | last5=Ziegler | first5=Günter | title=Oriented Matroids | edition=2nd | series=Encyclopedia of Mathematics and Its Applications | v ...

...allowing them to run efficiently without change on many different kinds of matroids, and without additional assumptions about what kind of matroid they are usi ...takes space exponential in <math> n</math>. Indeed, the number of distinct matroids on <math> n</math> elements grows [[double exponential function|doubly expo ...

| title = Lawrence oriented matroids and a problem of McMullen on projective equivalences of polytopes ...

...terising sparsity, matroids describe certain sets of sparse graphs. These matroids are connected to the [[structural rigidity]] of graphs and their ability to The first examples of sparsity matroids can be found in.<ref>{{Cite journal|last=Lorea|first=M.|date=1979-01-01|tit ...

| title = Convexity in oriented matroids ...

...e diagrams can also be described through the [[Dual matroid|duality]] of [[oriented matroid]]s.<ref>{{harvtxt|Ziegler|1995}}, Definition 6.17, p. 168</ref> ...

...<br /> [[Calculus of variation]] <br/> [[Stochastic programming]] <br/> [[Oriented matroid]] ...on theory]] and related fields of [[mathematical analysis|analysis]] and [[oriented matroid|combinatorics]]. He is the author of four major books including the ...

| title = Oriented Matroids ...