# nLab matroid

Matroid is one of the basic structures of combinatorics with several different ways of encoding/defining and presenting the generalization of the idea of a linearly independent basis in a vector space. There is also a similar concept of an oriented matroid; every oriented matroid has an underlying matroid.

Mnëv’s universality theorem says that any semialgebraic set in ${ℝ}^{n}$ defined over integers is stably equivalent to the realization space of some oriented matroid.

• wikipedia matroid, Mnëv’s universality theorem, oriented matroid
• Hassler Whitney, On the abstract properties of linear dependence, American Journal of Mathematics (The Johns Hopkins University Press) 57 (3): 509–533, 1935, jstor, MR1507091
• J. Oxley, What is a matroid, pdf
• James G. Oxley, Matroid theory, Oxford Grad. Texts in Math. 1992, 2010
• some papers on Coxeter matroids html
• MathOverflow question Mnëv’s universality corollaries, quantitative versions
• Eric Katz, Sam Payne, Realization space for tropical fans, pdf
• Nikolai E. Mnev, The universality theorems on the classification problem of configuration varieties and convex polytopes varieties, pp. 527-543, in “Topology and geometry: Rohlin Seminar.” Edited by O. Ya. Viro. Lecture Notes in Mathematics, 1346, Springer 1988; A lecture on universality theorem (in Russian) pdf
• Talal Ali Al-Hawary, Free objects in the category of geometries, pdf
• Talal Ali Al-Hawary, D. George McRae, Toward an elementary axiomatic theory of the category of LP-matroids, Applied Categorical Structures 11: 157–169, 2003, doi
• Hirokazu Nishimura, Susumu Kuroda, A lost mathematician, Takeo Nakasawa: the forgotten father of matroid theory 1996, 2009
• William H. Cunningham, Matching, matroids, and extensions, Math. Program., Ser. B 91: 515–542 (2002) doi
• L. Lovász, Matroid matching and some applications, J. Combinatorial Theory B 28, 208–236 (1980)
• A. Björner, M. Las Vergnas, B. Sturmfels, N. White, G.M. Ziegler, Oriented matroids, Cambridge Univ. Press 1993, 2000, view at reslib.com
Revised on April 19, 2012 19:42:53 by Gejza Jenca? (109.230.49.107)