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Experimental Mathematics Volume 9, 2000 - Issue 2
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Original Articles

Simplicial Manifolds, Bistellar Flips and a 16-Vertex Triangulation of the Poincaré Homology 3-Sphere

Anders Björner Department of Mathematics, Kungl, Tekniska Högskolan, S-100 44 Stockholm, Sweden E-mail: [email protected]
&
Frank H. Lutz Fachbereich Mathematik, Sekr.-MA 7-1, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany E-mail: [email protected]
Pages 275-289 | Published online: 04 Apr 2012

Citations (33)

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Francisco Criado & Francisco Santos. (2022) Topological Prismatoids and Small Simplicial Spheres of Large Diameter. Experimental Mathematics 31:2, pages 461-473.
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Bruno Benedetti & Frank H. Lutz. (2014) Random Discrete Morse Theory and a New Library of Triangulations. Experimental Mathematics 23:1, pages 66-94.
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Jonathan Spreer & Wolfgang Kühnel. (2011) Combinatorial Properties of the K3 Surface: Simplicial Blowups and Slicings. Experimental Mathematics 20:2, pages 201-216.
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Articles from other publishers (30)

Bruno Benedetti, Crystal Lai, Davide Lofano & Frank H. Lutz. (2023) Random simple-homotopy theory. Journal of Applied and Computational Topology.
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Romain Grunert, Wolfgang Kühnel & Günter Rote. (2023) PL Morse theory in low dimensions. Advances in Geometry 23:1, pages 135-150.
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Michael Joswig, Davide Lofano, Frank H. Lutz & Mimi Tsuruga. (2022) Frontiers of sphere recognition in practice. Journal of Applied and Computational Topology 6:4, pages 503-527.
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Davide Lofano & Andrew Newman. (2021) The worst way to collapse a simplex. Israel Journal of Mathematics 244:2, pages 625-647.
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Andrés Santamaría-Galvis & Russ Woodroofe. (2021) Shellings from Relative Shellings, with an Application to NP-Completeness. Discrete & Computational Geometry 66:2, pages 792-807.
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Radmila Sazdanovic & Victor Summers. (2021) Torsion in the magnitude homology of graphs. Journal of Homotopy and Related Structures 16:2, pages 275-296.
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Lorenzo Venturello & Hailun Zheng. (2020) A New Family of Triangulations of ℝPd. Combinatorica 41:1, pages 127-146.
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Christin Bibby, Andrew Odesky, Mengmeng Wang, Shuyang Wang, Ziyi Zhang & Hailun Zheng. (2020) Minimal flag triangulations of lower-dimensional manifolds. Involve, a Journal of Mathematics 13:4, pages 683-703.
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Frank H. Lutz & Jesper M. Møller. (2019) Chromatic Numbers of Simplicial Manifolds. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 61:3, pages 419-453.
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Biplab Basak & Ed Swartz. (2020) Three-dimensional normal pseudomanifolds with relatively few edges. Advances in Mathematics 365, pages 107035.
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Denis Gorodkov. (2019) A 15-Vertex Triangulation of the Quaternionic Projective Plane. Discrete & Computational Geometry 62:2, pages 348-373.
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Diamantino C. da Silva, Ginestra Bianconi, Rui A. da Costa, Sergey N. Dorogovtsev & José F. F. Mendes. (2018) Complex network view of evolving manifolds. Physical Review E 97:3.
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Karim A. Adiprasito, Bruno Benedetti & Frank H. Lutz. (2017) Extremal Examples of Collapsible Complexes and Random Discrete Morse Theory. Discrete & Computational Geometry 57:4, pages 824-853.
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Benjamin Burton & Jonathan Spreer. (2016) Combinatorial Seifert fibred spaces with transitive cyclic automorphism group. Israel Journal of Mathematics 214:2, pages 741-784.
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Jesper M. Møller & Gesche Nord. (2015) Chromatic Polynomials of Simplicial Complexes. Graphs and Combinatorics 32:2, pages 745-772.
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Jonathan Spreer. (2013) Combinatorial 3-Manifolds with Transitive Cyclic Symmetry. Discrete & Computational Geometry 51:2, pages 394-426.
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Michael Joswig, Frank H. Lutz & Mimi Tsuruga. 2014. Mathematical Software – ICMS 2014. Mathematical Software – ICMS 2014 152 159 .
Bhaskar Bagchi & Basudeb Datta. (2013) On -stellated and -stacked spheres . Discrete Mathematics 313:20, pages 2318-2329.
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Felix Effenberger & Jonathan Spreer. (2012) Simplicial blowups and discrete normal surfaces in simpcomp. ACM Communications in Computer Algebra 45:3/4, pages 173-176.
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Felix Effenberger. (2011) Stacked polytopes and tight triangulations of manifolds. Journal of Combinatorial Theory, Series A 118:6, pages 1843-1862.
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Felix Effenberger & Jonathan Spreer. (2011) simpcomp. ACM Communications in Computer Algebra 44:3/4, pages 186-189.
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Alexander A. Gaifullin. (2010) Configuration spaces, bistellar moves, and combinatorial formulae for the first Pontryagin class. Proceedings of the Steklov Institute of Mathematics 268:1, pages 70-86.
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Felix Effenberger & Wolfgang Kühnel. (2009) Hamiltonian Submanifolds of Regular Polytopes. Discrete & Computational Geometry 43:2, pages 242-262.
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Thom Sulanke & Frank H. Lutz. (2009) Isomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds. European Journal of Combinatorics 30:8, pages 1965-1979.
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Juan García Escudero. (2008) Random tilings of spherical 3-manifolds. Journal of Geometry and Physics 58:11, pages 1451-1464.
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Bhaskar Bagchi & Basudeb Datta. (2008) Lower bound theorem for normal pseudomanifolds. Expositiones Mathematicae 26:4, pages 327-351.
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Bhaskar Bagchi & Basudeb Datta. (2005) Combinatorial triangulations of homology spheres. Discrete Mathematics 305:1-3, pages 1-17.
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Francisco Santos. (2005) Non-connected toric Hilbert schemes. Mathematische Annalen 332:3, pages 645-665.
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Frank H. Lutz. (2004) Small Examples of Nonconstructible Simplicial Balls and Spheres. SIAM Journal on Discrete Mathematics 18:1, pages 103-109.
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Francisco Santos & Bernd Sturmfels. (2003) Alexander duality in subdivisions of Lawrence polytopes. Advances in Geometry 3:2.
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