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Published online by Cambridge University Press:  04 June 2025

Laura Anderson
Laura Anderson
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Oriented Matroids , pp. 310 - 316
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Abawonse, Olakunle S. 2023. Triangulations of Grassmannians and flag manifolds. Geom. Dedicata, 217(5), Paper No. 88, 25.CrossRefGoogle Scholar
Anderson, Laura. 1998. Homotopy groups of the combinatorial Grassmannian. Discrete Comput. Geom., 20(4), 549–560.CrossRefGoogle Scholar
Anderson, Laura. 1999. Topology of combinatorial differential manifolds. Topology, 38(1), 197–221.CrossRefGoogle Scholar
Anderson, Laura. 2001. Representing weak maps of oriented matroids. European J. Combin., 22(5), 579–586. Combinatorial geometries (Luminy, 1999).CrossRefGoogle Scholar
Anderson, Laura. 2019. Vectors of matroids over tracts. J. Combin. Theory Ser. A, 161, 236–270.Google Scholar
Anderson, Laura, and Davis, James F. 2001. There is no tame triangulation of the infinite real Grassmannian. Adv. Appl. Math., 26(3), 226–236.CrossRefGoogle Scholar
Anderson, Laura, and Davis, James F. 2002. Mod 2 cohomology of combinatorial Grassmannians. Selecta Math. (N.S.), 8(2), 161–200.CrossRefGoogle Scholar
Anderson, Laura, and Wenger, Rephael. 1996. Oriented matroids and hyperplane transversals. Adv. Math., 119(1), 117–125.CrossRefGoogle Scholar
Ardila, Federico, Rincón, Felipe, and Williams, Lauren. 2017. Positively oriented matroids are realizable. J. Eur. Math. Soc., 19(3), 815–833.CrossRefGoogle Scholar
Arkani-Hamed, Nima, Bourjaily, Jacob L., Cachazo, Freddy, Goncharov, Alexander B., Postnikov, Alexander, and Trnka, Jaroslav. 2014. Scattering amplitudes and the positive Grassmannian, https://arxiv.org/abs/1212.5605.Google Scholar
Arkani-Hamed, Nima, Bourjaily, Jacob, Cachazo, Freddy, Goncharov, Alexander B., Postnikov, Alexander, and Trnka, Jaroslav. 2016. Grassmannian geometry of scattering amplitudes. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Babson, Eric. 1994. A combinatorial flag space. PhD thesis, MIT.Google Scholar
Bachem, Achim, and Kern, Walter. 1986. Adjoints of oriented matroids. Combinatorica, 6(4), 299–308.CrossRefGoogle Scholar
Bachem, Achim, and Kern, Walter. 1992. Linear programming duality. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Bachem, Achim, and Wanka, Alfred. 1988. Separation theorems for oriented matroids. Discrete Math., 70(3), 303–310.CrossRefGoogle Scholar
Baker, Matthew, and Bowler, Nathan. 2019. Matroids over partial hyperstructures. Adv. Math., 343, 821–863.CrossRefGoogle Scholar
Barmak, Jonathan Ariel. 2011. On Quillen’s Theorem A for posets. J. Combin. Theory Ser. A, 118(8), 2445–2453.CrossRefGoogle Scholar
Bayer, Margaret, and Sturmfels, Bernd. 1990. Lawrence polytopes. Canad. J. Math., 42(1), 62–79.CrossRefGoogle Scholar
Belkale, Prakash, and Brosnan, Patrick. 2003. Matroids, motives, and a conjecture of Kontsevich. Duke Math. J., 116(1), 147–188.CrossRefGoogle Scholar
Billera, Louis J., and Munson, Beth Spellman. 1984a. Oriented matroids and triangulations of convex polytopes. In Progress in combinatorial optimization (Waterloo, Ont., 1982). Toronto, ON: Academic Press, pp. 27–37.CrossRefGoogle Scholar
Billera, Louis J., and Munson, Beth Spellman. 1984b. Polarity and inner products in oriented matroids. European J. Combin., 5(4), 293–308.CrossRefGoogle Scholar
Billera, Louis J., and Munson, Beth Spellman. 1984c. Triangulations of oriented matroids and convex polytopes. SIAM J. Algebraic Discrete Meth., 5(4), 515–525.CrossRefGoogle Scholar
Biss, Daniel K. 2003. The homotopy type of the matroid Grassmannian. Ann. Math. (2), 158(3), 929–952.CrossRefGoogle Scholar
Biss, Daniel K. 2009. Erratum to “The homotopy type of the matroid Grassmannian” [MR2031856]. Ann. Math. (2), 170(1), 493.CrossRefGoogle Scholar
Björner, Anders. 1995. Topological methods. In Handbook of combinatorics, Vol. 1, 2, (eds.) Graham, R. L., Grötschel, M., and Lovász, L.. Amsterdam: Elsevier, pp. 1819–1872.Google Scholar
Björner, Anders, Las Vergnas, Michel, Sturmfels, Bernd, White, Neil, and Ziegler, Günter M. 1999. Oriented matroids, 2nd ed. Encyclopedia of Mathematics and Its Applications, vol. 46. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Bland, Robert G. 1977. A combinatorial abstraction of linear programming. J. Combin. Theory Ser. B, 23(1), 33–57.CrossRefGoogle Scholar
Bland, Robert G., and Dietrich, Brenda L. 1988. An abstract duality. Discrete Math., 70(2), 203–208.CrossRefGoogle Scholar
Bland, Robert G., and Las Vergnas, Michel. 1978. Orientability of matroids. J. Combin. Theory Ser. B., 24(1), 94–123.CrossRefGoogle Scholar
Bland, Robert G., and Las Vergnas, Michel. 1979. Minty colorings and orientations of matroids. In Second International Conference on Combinatorial Mathematics (New York, 1978). Annals of the New York Academy of Sciences, vol. 319. New York: New York Academy of Sciences, pp. 86–92.Google Scholar
Boege, T. n.d. On stable equivalence of semialgebraic sets. https://taboege.de/blog/2022/02/On-stable-equivalence-of-semialgebraic-sets, accessed: 2023-02-08.Google Scholar
Bokowski, Jürgen G. 2006. Computational oriented matroids. Cambridge: Cambridge University Press.Google Scholar
Bokowski, Jürgen, and Sturmfels, Bernd. 1989. Computational synthetic geometry. Lecture Notes in Mathematics, vol. 1355. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Bruggesser, H., and Mani, P. 1971. Shellable decompositions of cells and spheres. Math. Scand., 29, 197–205.CrossRefGoogle Scholar
Büchi, J. Richard, and Fenton, William E. 1988. Large convex sets in oriented matroids. J. Combin. Theory Ser. B, 45(3), 293–304.CrossRefGoogle Scholar
Buchstaber, Victor M., and Panov, Taras E. 2002. Torus actions and their applications in topology and combinatorics. University Lecture Series, vol. 24. Providence, RI: American Mathematical Society.Google Scholar
Cordovil, Raul. 1987. Polarity and point extensions in oriented matroids. Linear Algebra Appl., 90, 15–31.CrossRefGoogle Scholar
da Silva, Ilda. 1987. Quelques propriétés des matroïdes orientés. PhD thesis, Université de Paris VI.Google Scholar
da Silva, Ilda. 1995. Axioms for maximal vectors of an oriented matroid; a combinatorial characterization of the regions determined by an arrangement of pseudohyperplanes. European J. Combin., 16(2), 125–145.CrossRefGoogle Scholar
Dobbins, Michael Gene. 2011. Representations of polytopes. PhD thesis, Temple University.Google Scholar
Edelman, Paul H. 1984. The acyclic sets of an oriented matroid. J. Combin. Theory Ser. B, 36(1), 26–31.CrossRefGoogle Scholar
Folkman, Jon, and Lawrence, Jim. 1978. Oriented matroids. J. Combin. Theory Ser. B, 25(2), 199–236.CrossRefGoogle Scholar
Fukuda, Komei. 1982. Oriented matroid programming. PhD thesis, University of Waterloo (Canada).Google Scholar
Fukuda, Komei, and Tamura, Akihisa. 1990. Dualities in signed vector systems. Portugal. Math., 47(2), 151–165.Google Scholar
Galashin, Pavel, Karp, Steven N., and Lam, Thomas. 2022. The totally nonnegative Grassmannian is a ball. Adv. Math., 397, Paper No. 108123, 23.CrossRefGoogle Scholar
Geelen, Jim, Gerards, Bert, and Whittle, Geoff. 2014. Solving Rota’s conjecture. Notices Amer. Math. Soc., 61(7), 736–743.CrossRefGoogle Scholar
Gel’fand, Israel M., and MacPherson, Robert D. 1982. Geometry in Grassmannians and a generalization of the dilogarithm. Adv. Math., 44(3), 279–312.CrossRefGoogle Scholar
Gel’fand, Israel M., and MacPherson, Robert D. 1992. A combinatorial formula for the Pontrjagin classes. Bull. Amer. Math. Soc. (N.S.), 26(2), 304–309.CrossRefGoogle Scholar
Gel’fand, Israel M., and Serganova, Vera V. 1987. Combinatorial geometries and the strata of a torus on homogeneous compact manifolds. Uspekhi Mat. Nauk, 42(2), 107–134.Google Scholar
Gel’fand, Israel M., Goresky, R. Mark, MacPherson, Robert D., and Serganova, Vera V. 1987. Combinatorial geometries, convex polyhedra, and Schubert cells. Adv. Math., 63(3), 301–316.CrossRefGoogle Scholar
Goodman, Jacob E., and Pollack, Richard. 1980a. On the combinatorial classification of nondegenerate configurations in the plane. J. Combin. Theory Ser. A, 29(2), 220–235.CrossRefGoogle Scholar
Goodman, Jacob E., and Pollack, Richard. 1980b. Proof of Grünbaum’s conjecture on the stretchability of certain arrangements of pseudolines. J. Combin. Theory Ser. A, 29(3), 385–390.CrossRefGoogle Scholar
Hatcher, Allen. 2002.Algebraic topology. Cambridge: Cambridge University Press.Google Scholar
Higgs, Denis A. 1968. Strong maps of geometries. J. Combin. Theory, 5, 185–191.CrossRefGoogle Scholar
Hironaka, Heisuke. 1975. Triangulations of algebraic sets. In Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974). Providence, RI: American Mathematical Society, pp. 165–185.CrossRefGoogle Scholar
Hudson, John F. P. 1969. Piecewise linear topology. University of Chicago Lecture Notes prepared with the assistance of J. L. Shaneson and J. Lees. New York/Amsterdam: W. A. Benjamin.Google Scholar
Jaggi, Beat, and Mani-Levitska, Peter. 1988. A simple arrangement of lines without the isotopy property. preprint, Univ. Bern. 28 pages.Google Scholar
Jaggi, Beat, Mani-Levitska, Peter, Sturmfels, Bernd, and White, Neil. 1989. Uniform oriented matroids without the isotopy property. Discrete Comput. Geom., 4(2), 97–100.CrossRefGoogle Scholar
Jarra, Manoel, and Lorscheid, Oliver. 2024.Flag matroids with coefficients. Adv. Math. 436, Paper No. 109396, 46, DOI: 10.1016∕j.aim.2023.109396.Google Scholar
Kapovich, Michael, and Millson, John J. 1998. On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties. Inst. Hautes Études Sci. Publ. Math., 88, 5–95.CrossRefGoogle Scholar
Kung, Joseph P. S. 1983. A characterization of orthogonal duality in matroid theory. Geom. Dedicata, 15(1), 69–72.CrossRefGoogle Scholar
Kung, Joseph P. S., Rota, Gian-Carlo, and Yan, Catherine H. 2009. Combinatorics: the Rota way. Cambridge Mathematical Library. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Lafforgue, L. 2003.Chirurgie des grassmanniennes. CRM Monograph Series, vol. 19. Providence, RI: American Mathematical Society.CrossRefGoogle Scholar
Las, Vergnas, Michel. 1975a. Coordinatizable strong maps of matroids. preprint, 123 pages.Google Scholar
Las Vergnas, Michel. 1975b. Matroïdes orientables. C. R. Acad. Sci. Paris Sér A-B, 280, Ai, A61–A64.Google Scholar
Las, Vergnas, Michel. 1978. Extensions ponctuelles d’une géométrie combinatoire orientée. In Problèmes combinatoires et théorie des graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976). Colloq. Internat. CNRS, vol. 260. Paris: CNRS, pp. 265–270.Google Scholar
Las Vergnas, Michel. 1980. Convexity in oriented matroids. J. Combin. Theory Ser. B, 29(2), 231–243.CrossRefGoogle Scholar
Las Vergnas, Michel. 1984. Oriented matroids as signed geometries real in corank 2. In Finite and infinite sets, Vol. I, II (Eger, 1981), (eds.) Hajnal, András, Lovász, László, and Sós, Vera T.. Colloq. Math. Soc. János Bolyai, vol. 37. North-Holland, Amsterdam, pp. 555–565.Google Scholar
Lawrence, Jim. 1983. Lopsided sets and orthant-intersection by convex sets. Pacific J. Math., 104(1), 155–173.CrossRefGoogle Scholar
Lawrence, Jim. 1984.Shellability of oriented matroid complexes. preprint, 8 pages.Google Scholar
Lee, Seok Hyeong, and Vakil, Ravi. 2013. Mnëv-Sturmfels universality for schemes. In A celebration of algebraic geometry. Clay Math. Proc., vol. 18. Providence, RI: American Mathematical Society, pp. 457–468.Google Scholar
Levi, Friedrich. 1926. Die Teilung der projektiven Ebene durch Gerade oder Pseudogerade. Ber. Math.-Phys. Kl. Sachs. Akad. Wiss., 78, 256–267.Google Scholar
Liu, Gaku. 2020. A counterexample to the extension space conjecture for realizable oriented matroids. J. Lond. Math. Soc. (2), 101(1), 175–193.CrossRefGoogle Scholar
MacPherson, Robert. 1993. Combinatorial differential manifolds. In Topological methods in modern mathematics (Stony Brook, NY, 1991). Houston, TX: Publish or Perish, pp. 203–221.Google Scholar
Mandel, Arnaldo. 1982. Topology of oriented matroids. PhD thesis, University of Waterloo.Google Scholar
Mayhew, Dillon, Whittle, Geoff, and Newman, Mike. 2014. Is the missing axiom of matroid theory lost forever? Q. J. Math., 65(4), 1397–1415.CrossRefGoogle Scholar
Mayhew, Dillon, Newman, Mike, and Whittle, Geoff. 2018. Yes, the ‘missing axiom’ of matroid theory is lost forever. Trans. Amer. Math. Soc., 370(8), 5907–5929.CrossRefGoogle Scholar
McCord, Michael C. 1967. Homotopy type comparison of a space with complexes associated with its open covers. Proc. Amer. Math. Soc., 18, 705–708.CrossRefGoogle Scholar
Milnor, John W., and Stasheff, James D. 1974. Characteristic classes. Annals of Mathematics Studies, No. 76. Princeton, NJ: Princeton University Press; Tokyo: University of Tokyo Press.CrossRefGoogle Scholar
Minty, George J. 1966. On the axiomatic foundations of the theories of directed linear graphs, electrical networks and network-programming. J. Math. Mech., 15, 485–520.Google Scholar
Mnëv, Nikolai E. Brief history of Universality theorem for moduli spaces of line arrangements. www.pdmi.ras.ru/mnev/bhu.html, accessed: March 30, 2022.Google Scholar
Mnëv, Nikolai E. 1986. The topology of configuration varieties and convex polytopes varieties. PhD thesis, Leningrad State University. [In Russian]Google Scholar
Mnëv, Nikolai E. 1988. The universality theorems on the classification problem of configuration varieties and convex polytopes varieties. In Topology and geometry— Rohlin Seminar, (eds.) Yanovich Viro, Oleg and Vershik, Anatoly Moiseevich. Lecture Notes in Math., vol. 1346. Berlin: Springer, pp. 527–543.CrossRefGoogle Scholar
Mnëv, Nicolai E., and Richter-Gebert, Jürgen. 1993. Two constructions of oriented matroids with disconnected extension space. Discrete Comput. Geom., 10(3), 271–285.CrossRefGoogle Scholar
Munkres, James R. 1984.Elements of algebraic topology. Menlo Park, CA: Addison-Wesley.Google Scholar
Munson, Beth Spellman. 1981. Face lattices of oriented matroids. PhD thesis, Cornell University.Google Scholar
Oxley, James G. 1992. Matroid theory. Oxford Science Publications. New York: The Clarendon Press; Oxford University Press.Google Scholar
Postnikov, Alexander. 2006.Total positivity, Grassmannians, and networks. https://arxiv.org/abs/math/0609764Google Scholar
Postnikov, Alexander, Speyer, David, and Williams, Lauren. 2009. Matching polytopes, toric geometry, and the totally non-negative Grassmannian. J. Algebraic Combin., 30(2), 173–191.CrossRefGoogle Scholar
Quillen, Daniel. 1973. Higher algebraic K-theory. I. In Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972). Lecture Notes in Math., vol. 341. Berlin: Springer, pp. 85–147.Google Scholar
Rambau, Jörg. 2002. Circuit admissible triangulations of oriented matroids. Geometric combinatorics (San Francisco, CA/Davis, CA, 2000). Discrete Comput. Geom., 27, 155–161.CrossRefGoogle Scholar
Richter-Gebert, Jürgen. 1988. Kombinatorische Realisierbarkeitskriterien für orientierte Matroide. MPhil thesis, TU Darmstadt.Google Scholar
Richter-Gebert, Jürgen. 1989. Kombinatorische Realisierbarkeitskriterien für orientierte Matroide. (Criteria for the realizability of oriented matroids). Mitt. Math. Semin. Gießen, 194, 1–112.Google Scholar
Richter-Gebert, Jürgen. 1993. Oriented matroids with few mutations. Discrete Comput. Geom., 10(3), 251–269.CrossRefGoogle Scholar
Richter-Gebert, Jürgen. 1996a. Realization spaces of polytopes. Lecture Notes in Mathematics, vol. 1643. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Richter-Gebert, Jürgen. 1996b. Two interesting oriented matroids. Doc. Math., 1, No. 07, 137–148.CrossRefGoogle Scholar
Richter-Gebert, Jürgen and Ziegler, Günter M. 1994. Zonotopal tilings and the Bohne-Dress theorem. In Jerusalem combinatorics ’93. Contemp. Math., vol. 178. Providence, RI: American Mathematical Society, pp. 211–232.CrossRefGoogle Scholar
Ringel, Gerhard. 1956. Teilungen der Ebene durch Geraden oder topologische Geraden. Math. Z., 64, 79–102.CrossRefGoogle Scholar
Rockafellar, R. Tyrell. 1969. The elementary vectors of a subspace of RN. In Combinatorial mathematics and its applications (Proc. Conf., Univ. North Carolina, Chapel Hill, N.C., 1967). Chapel Hill, NC: University of North Carolina Press, pp. 104–127.Google Scholar
Rourke, Colin Patrick, and Sanderson, Brian Joseph. 1982. Introduction to piecewise-linear topology. Springer Study Edition. Berlin/New York: Springer-Verlag.Google Scholar
Santos, Francisco. 2002. Triangulations of oriented matroids. Mem. Amer. Math. Soc., 156(741), viii+80.Google Scholar
Scott, Joshua S. 2006. Grassmannians and cluster algebras. Proc. London Math. Soc. (3), 92(2), 345–380.CrossRefGoogle Scholar
Seymour, Paul D. 1979. Matroid representation over GF(3). J. Combin. Theory Ser. B, 26(2), 159–173.CrossRefGoogle Scholar
Shor, Peter W. 1991. Stretchability of pseudolines is NP-hard. In Applied geometry and discrete mathematics, (eds.) Sturmfels, Bernd and Gritzman, Peter. DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 4. Providence, RI: American Mathematical Society. pp. 531–554.Google Scholar
Stanley, Richard P. 1997.Enumerative combinatorics. Vol. 1. Cambridge Studies in Advanced Mathematics, vol. 49. Cambridge: Cambridge University Press. With a foreword by Gian-Carlo Rota, corrected reprint of the 1986 original.CrossRefGoogle Scholar
Sturmfels, Bernd. 1988. Some applications of affine Gale diagrams to polytopes with few vertices. SIAM J. Discrete Math., 1(1), 121–133.CrossRefGoogle Scholar
Sturmfels, Bernd. 1989. On the matroid stratification of Grassmann varieties, specialization of coordinates, and a problem of N. White. Adv. Math., 75(2), 202–211.CrossRefGoogle Scholar
Sturmfels, Bernd, and Ziegler, Günter M. 1993. Extension spaces of oriented matroids. Discrete Comput. Geom., 10(1), 23–45.CrossRefGoogle Scholar
Suvorov, P. 1988. Isotopic but not rigidly isotopic plane systems of straight lines. In Topology and geometry—Rohlin Seminar, (eds.) Yanovich Viro, Oleg. Lecture Notes in Math., vol. 1346. Berlin: Springer. pp. 545–556.CrossRefGoogle Scholar
Tsukamoto, Yasuyuki. 2013. New examples of oriented matroids with disconnected realization spaces. Discrete Comput. Geom., 49(2), 287–295.CrossRefGoogle Scholar
Tutte, W. T. 1958. A homotopy theorem for matroids. I, II. Trans. Amer. Math. Soc., 88, 144–174.Google Scholar
Vakil, Ravi. 2006. Murphy’s law in algebraic geometry: badly-behaved deformation spaces. Invent. Math., 164(3), 569–590.CrossRefGoogle Scholar
Vámos, Peter. 1978. The missing axiom of matroid theory is lost forever. J. London Math. Soc. (2), 18(3), 403–408.CrossRefGoogle Scholar
Verkama, Emil. 2023. Repairing the Universality Theorem for 4-polytopes. MPhil thesis, Aalto University.Google Scholar
Vershik, Anatoliĭ M. 1988. Topology of the convex polytopes’ manifolds, the manifold of the projective configurations of a given combinatorial type and representations of lattices. In Topology and geometry—Rohlin Seminar. Lecture Notes in Math., vol. 1346, (eds.) Viro, Oleg Yanovich. Berlin: Springer. pp. 557–581.CrossRefGoogle Scholar
Walker, James W. 1981. Homotopy type and Euler characteristic of partially ordered sets. European J. Combin., 2(4), 373–384.CrossRefGoogle Scholar
White, Neil L. 1989. A nonuniform matroid which violates the isotopy conjecture. Discrete Comput. Geom., 4(1), 1–2.CrossRefGoogle Scholar
Whitney, Hassler. 1935. On the abstract properties of linear dependence. Amer. J. Math, 57(3), 509–533.CrossRefGoogle Scholar
Winder, Robert O. 1966. Partitions of N-space by hyperplanes. SIAM J. Appl. Math., 14, 811–818.CrossRefGoogle Scholar
Wu, Pei. 2021. A counterexample to Las Vergnas’ strong map conjecture on realizable oriented matroids. Discrete Comput. Geom., 65(1), 143–149.CrossRefGoogle Scholar
Zaslavsky, Thomas. 1975. Facing up to arrangements: face-count formulas for partitions of space by hyperplanes. Mem. Amer. Math. Soc., 1(1), vii+102.Google Scholar
Zaslavsky, Thomas. 1977. A combinatorial analysis of topological dissections. Adv. Math., 25(3), 267–285.CrossRefGoogle Scholar
Živaljević, Rade T. 2016. On the continuous combinatorics of posets, polytopes and matroids. Fundam. Prikl. Mat., 21(6), 143–164.Google Scholar
Ziegler, Günter M. 1991. Some minimal nonorientable matroids of rank three. Geom. Dedicata, 38(3), 365–371.CrossRefGoogle Scholar
Ziegler, Günter M. 1995. Lectures on polytopes. Graduate Texts in Mathematics, vol. 152. New York: Springer-Verlag.CrossRefGoogle Scholar

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  • References
  • Laura Anderson, Binghamton University, New York
  • Book: Oriented Matroids
  • Online publication: 04 June 2025
  • Chapter DOI: https://doi.org/10.1017/9781009494076.013
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  • References
  • Laura Anderson, Binghamton University, New York
  • Book: Oriented Matroids
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  • Laura Anderson, Binghamton University, New York
  • Book: Oriented Matroids
  • Online publication: 04 June 2025
  • Chapter DOI: https://doi.org/10.1017/9781009494076.013
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