Content deleted Content added
m →History: Fixing links to disambiguation pages, improving links, other minor cleanup tasks |
|||
Line 39:
A [[matroid]] is a structure that captures and generalizes the notion of [[linear independence]] in [[vector space]]s. There are many equivalent ways to define a matroid, the most significant being in terms of independent sets, bases, circuits, closed sets or flats, closure operators, and rank functions.
Matroid theory borrows extensively from the terminology of [[linear algebra]] and [[graph theory]], largely because it is the abstraction of various notions of central importance in these fields. Matroids have found applications in geometry, [[topology]], [[combinatorial optimization]], [[network theory]] and [[coding theory]].<ref name=Neel2009>{{cite journal|last1=Neel|first1=David L.|last2=Neudauer|first2=Nancy Ann|author2-link= Nancy Neudauer |title=Matroids you have known|journal=Mathematics Magazine|date=2009|volume=82|issue=1|pages=26–41|url=http://www.maa.org/sites/default/files/pdf/shortcourse/2011/matroidsknown.pdf|accessdate=4 October 2014|doi=10.4169/193009809x469020}}</ref><ref name=Kashyap2009>{{cite web|last1=Kashyap|first1=Navin|last2=Soljanin|first2=Emina|last3=Vontobel|first3=Pascal|title=Applications of Matroid Theory and Combinatorial Optimization to Information and Coding Theory|url=https://www.birs.ca/workshops/2009/09w5103/report09w5103.pdf|website=www.birs.ca|accessdate=4 October 2014}}</ref>
===Finite geometries===
| |||