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A sweep of a point configuration is any ordered partition induced by a linear functional.
Robert P. Dilworth, Dependence relations in a semi-modular lattice , Duke Math. J. 11
1944
Earlier work this paper cites.
Saul Gass and Thomas Saaty, The computational algorithm for the parametric objective function , Naval Res. Logist. Quart. 2
1955
Earlier work this paper cites.
Jacques Tits, Le problème des mots dans les groupes de Coxeter , Symposia Mathematica (INDAM, Rome, 1967/68), Vol. 1, Academic Press, London, 1969, pp. 175–185
1969
Earlier work this paper cites.
Heinz Bruggesser and Peter Mani, Shellable decompositions of cells and spheres , Math. Scand. 29
1971
Earlier work this paper cites.
Richard P. Stanley, Modular elements of geometric lattices , Algebra Universalis 1
1971
Earlier work this paper cites.
Pierre Deligne, Les immeubles des groupes de tresses généralisés , Invent. Math. 17
1972
Earlier work this paper cites.
by same author, Supersolvable lattices , Algebra Universalis 2
1972
Earlier work this paper cites.
Tom Brylawski, Modular constructions for combinatorial geometries , Trans. Amer. Math. Soc. 203
1975
Earlier work this paper cites.
John H. Mason, Matroids as the study of geometrical configurations , Higher combinatorics (Proc. NATO Advanced Study Inst., Berlin, 1976), NATO Adv. Study Inst. Ser., Ser. C: Math. Phys. Sci., vol. 31, Reidel, Dordrecht-Boston, Mass., 1977, pp. 133–176. MR 519783
1977
Earlier work this paper cites.
Daniel Quillen, Homotopy properties of the poset of nontrivial p p -subgroups of a group , Adv. in Math. 28
1978
Earlier work this paper cites.
Jacob E. Goodman and Richard Pollack, On the combinatorial classification of nondegenerate configurations in the plane , J. Combin. Theory Ser. A 29
1980
Earlier work this paper cites.
by same author, Proof of Grünbaum’s conjecture on the stretchability of certain arrangements of pseudolines , Journal of Combinatorial Theory, Series A 29
1980
Earlier work this paper cites.
Jack Edmonds and Arnaldo Mandel, Topology of oriented matroids, Ph.D. Thesis of A. Mandel , Ph.D. thesis, University of Waterloo, 1982
1982
Earlier work this paper cites.
by same author, A theorem of ordered duality , Geom. Dedicata 12
1982
Earlier work this paper cites.
Peter Ungar, 2 N 2N noncollinear points determine at least 2 N 2N directions , J. Combin. Theory Ser. A 33
1982
Earlier work this paper cites.
Anders Björner, Posets, regular CW complexes and Bruhat order , European J. Combin. 5
1984
Earlier work this paper cites.
by same author, Semispaces of configurations, cell complexes of arrangements , J. Combin. Theory Ser. A 37
1984
Earlier work this paper cites.
by same author, On the number of reduced decompositions of elements of Coxeter groups , European J. Combin. 5
1984
Earlier work this paper cites.
Noga Alon and Ervin Győri, The number of small semispaces of a finite set of points in the plane , J. Combin. Theory Ser. A 41
1986
Earlier work this paper cites.
Thomas Brylawski, Constructions , Theory of matroids, Encyclopedia Math. Appl., vol. 26, Cambridge Univ. Press, Cambridge, 1986, pp. 127–223
1986
Earlier work this paper cites.
Herbert Edelsbrunner, Joseph O’Rourke, and Raimund Seidel, Constructing arrangements of lines and hyperplanes with applications , SIAM Journal on Computing 15
1986
Earlier work this paper cites.
Joseph P. S. Kung and Hien Q. Nguyen, Weak maps , Theory of matroids, Encyclopedia Math. Appl., vol. 26, Cambridge Univ. Press, Cambridge, 1986, pp. 254–271
1986
Earlier work this paper cites.
Emo Welzl, More on k k -sets of finite sets in the plane , Discrete Comput. Geom. 1
1986
Earlier work this paper cites.
Neil White (ed.), Theory of matroids , Encyclopedia of Mathematics and its Applications, vol. 26, Cambridge University Press, Cambridge, 1986
1986
Earlier work this paper cites.
Karl-Heinz Borgwardt, The simplex method , Algorithms and Combinatorics: Study and Research Texts, vol. 1, Springer-Verlag, Berlin, 1987, A probabilistic analysis
1987
Earlier work this paper cites.
Paul Edelman and Curtis Greene, Balanced tableaux , Adv. in Math. 63
1987
Earlier work this paper cites.
Mario Salvetti, Topology of the complement of real hyperplanes in 𝐂 N {\bf C}^{N} , Invent. Math. 88
1987
Earlier work this paper cites.
Abraham Berman and Anton Kotzig, Cross-cloning and antipodal graphs , Discrete Math. 69
1988
Earlier work this paper cites.
N. E. Mnëv, The universality theorems on the classification problem of configuration varieties and convex polytopes varieties , Topology and geometry—Rohlin Seminar, Lecture Notes in Math., vol. 1346, Springer, Berlin, 1988, pp. 527–543
1988
Earlier work this paper cites.
Herbert Edelsbrunner and Leonidas J Guibas, Topologically sweeping an arrangement , Journal of Computer and System Sciences 38
1989
Earlier work this paper cites.
Yuri I. Manin and Vadim V. Schechtman, Arrangements of hyperplanes, higher braid groups and higher Bruhat orders , Algebraic number theory, Adv. Stud. Pure Math., vol. 17, Academic Press, Boston, MA, 1989, pp. 289–308
1989
Cited alongside, same era.
Günter M. Ziegler, The face lattice of hyperplane arrangements , Proceedings of the Oberwolfach Meeting “Kombinatorik” (1986), vol. 73, 1989, pp. 223–238
1989
Cited alongside, same era.
Anders Björner, Paul H. Edelman, and Günter M. Ziegler, Hyperplane arrangements with a lattice of regions , Discrete Comput. Geom. 5
1990
Cited alongside, same era.
Raul Cordovil and Maria Leonor Moreira, A homotopy theorem on oriented matroids , Discrete Math. 111
1990
Cited alongside, same era.
Komei Fukuda and Keiichi Handa, Antipodal graphs and oriented matroids , Discrete Math. 111
1990
Cited alongside, same era.
Christos A. Athanasiadis and Francisco Santos, Monotone paths on zonotopes and oriented matroids , Canad. J. Math. 53
2001
Later among the works it cites.
Stefan Felsner and Helmut Weil, Sweeps, arrangements and signotopes , Discrete Appl. Math. 109
2001
Later among the works it cites.
Stefan Felsner and Günter M. Ziegler, Zonotopes associated with higher Bruhat orders , Discrete Math. 241
2001
Later among the works it cites.
Allen Hatcher, Algebraic topology , Cambridge University Press, Cambridge, 2002
2002
Later among the works it cites.
Jiří Matoušek, Lectures on discrete geometry , Graduate Texts in Mathematics, vol. 212, Springer-Verlag, New York, 2002
2002
Later among the works it cites.
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Keiichi Handa, A characterization of oriented matroids in terms of topes , European J. Combin. 11
1990
Cited alongside, same era.
Jack Snoeyink and John Hershberger, Sweeping arrangements of curves , Discrete and computational geometry (New Brunswick, NJ, 1989/1990), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 6, Amer. Math. Soc., Providence, RI, 1991, pp. 309–349
1991
Cited alongside, same era.
by same author, Essential chains and homotopy type of posets , Proc. Amer. Math. Soc. 116
1992
Cited alongside, same era.
Louis J. Billera and Bernd Sturmfels, Fiber polytopes , Annals of Mathematics (1992), 527–549
1992
Cited alongside, same era.
by same author, Allowable sequences and order types in discrete and computational geometry , New trends in discrete and computational geometry, Algorithms Combin., vol. 10, Springer, Berlin, 1993, pp. 103–134
1993
Cited alongside, same era.
Peter Gritzmann and Bernd Sturmfels, Minkowski addition of polytopes: computational complexity and applications to Gröbner bases , SIAM J. Discrete Math. 6
1993
Cited alongside, same era.
by same author, Topes of oriented matroids and related structures , Publ. Res. Inst. Math. Sci. 29
1993
Cited alongside, same era.
2003
Later among the works it cites.
Stefan Felsner, Geometric graphs and arrangements , Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Wiesbaden, 2004, Some chapters from combinatorial geometry
2004
Later among the works it cites.
László Lovász, Katalin Vesztergombi, Uli Wagner, and Emo Welzl, Convex quadrilaterals and k k -sets , Towards a theory of geometric graphs, Contemp. Math., vol. 342, Amer. Math. Soc., Providence, RI, 2004, pp. 139–148
2004
Later among the works it cites.
Anders Björner and Francesco Brenti, Combinatorics of Coxeter groups , Graduate Texts in Mathematics, vol. 231, Springer, New York, 2005
2005
Later among the works it cites.
Peter McMullen, Fibre tilings , Mathematika 50
2005
Later among the works it cites.
Joseph E. Bonin, Extending a matroid by a cocircuit , Discrete Math. 306
2006
Later among the works it cites.
Jiří Matoušek and Bernd Gärtner, Understanding and using linear programming (universitext) , Springer-Verlag, Berlin, Heidelberg, 2006
2006
Later among the works it cites.
Omer Angel, Alexander E. Holroyd, Dan Romik, and Bálint Virág, Random sorting networks , Adv. Math. 215
2007
Later among the works it cites.
Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars, Computational geometry , third ed., Springer-Verlag, Berlin, 2008, Algorithms and applications
2008
Later among the works it cites.
Alexander Postnikov, Permutohedra, associahedra, and beyond , Int. Math. Res. Not. IMRN (2009), no. 6, 1026–1106
2009
Later among the works it cites.
Jesus A. De Loera, Jörg Rambau, and Francisco Santos, Triangulations: Structures for algorithms and applications , Algorithms and Computation in Mathematics, vol. 25, Springer Verlag, 2010
2010
Later among the works it cites.
Victor Reiner and Yuval Roichman, Diameter of graphs of reduced words and galleries , Trans. Amer. Math. Soc. 365
2013
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by same author, Valid orderings of real hyperplane arrangements , Discrete Comput. Geom. 53
2015
Later among the works it cites.
Winfried Hochstättler, Topological sweeping in oriented matroids , Technical report https://www.fernuni-hagen.de/MATHEMATIK/DMO/pubs/feu-dmo042-16.pdf , 2016
2016
Later among the works it cites.
Hans-Jürgen Bandelt, Victor Chepoi, and Kolja Knauer, COMs: complexes of oriented matroids , J. Combin. Theory Ser. A 156
2018
Later among the works it cites.
2018
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Omer Angel, Duncan Dauvergne, Alexander E. Holroyd, and Bálint Virág, The local limit of random sorting networks , Ann. Inst. Henri Poincaré Probab. Stat. 55
2019
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2020
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Kolja Knauer and Tilen Marc, On Tope Graphs of Complexes of Oriented Matroids , Discrete Comput. Geom. 63
2020
Later among the works it cites.
Rob Edman, Pakawut Jiradilok, Gaku Liu, and Thomas McConville, Zonotopes whose cellular strings are all coherent , 2021
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