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 defined over integers is stably equivalent to the realization space of some oriented matroid.
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?