1. Ewgenij Gawrilow and Michael Joswig. polymake: a framework for analyzing convex polytopes. Polytopes—combinatorics and computation (Oberwolfach, 1997), 43–73, DMV Sem., 29, Birkhäuser, Basel, 2000. MR1785292 (2001f:52033)
  2. Ewgenij Gawrilow and Michael Joswig. polymake: an approach to modular software design in computational geometry, Proceedings of the 17th Annual Symposium on Computational Geometry, 222–231. ACM, 2001.
  3. Ewgenij Gawrilow and Michael Joswig. Geometric reasoning with polymake. In: Kurt Kremer and Volker Macho, eds., Forschung und wissenschaftliches Rechnen 2005: Beiträge zum Heinz-Billing-Preis 2005, Gesellschaft für wissenschaftliche Datenverarbeitung mbh Göttingen, Bericht Nr. 69, 37–52. Preprint arXiv:math.CO/0507273.
  4. Michael Joswig, Benjamin Müller, and Andreas Paffenholz. Polymake and Lattice Polytopes, Proceedings of the 21th International Conference on Formal Power Series and Algebraic Combinatorics (2009), 493–504. dmAK0141/2751
  5. Ewgenij Gawrilow, Michael Joswig, Thilo Rörig, and Nikolaus Witte. Drawing polytopal graphs with polymake, Computing and Visualization in Science 13 (2010), no. 2, 99–110 DOI:10.1007/s00791-009-0127-3
  6. Sven Herrmann, Michael Joswig, and Marc E. Pfetsch. Computing the bounded subcomplex of an unbounded polyhedron. arXiv:1006.2767
  7. Michael Joswig and Andreas Paffenholz. Defect Polytopes and Counter-Examples With polymake. arXiv:1105.0527
  8. Benjamin Assarf , Ewgenij Gawrilow, Katrin Herr, Michael Joswig, Benjamin Lorenz, Andreas Paffenholz and Thomas Rehn, polymake in Linear and Integer Programming, arXiv:1408.4653
  1. Michael Joswig and Günter M. Ziegler. Neighborly cubical polytopes. The Branko Grünbaum birthday issue. Discrete Comput. Geom. 24 (2000), no. 2-3, 325–344. MR1758054 (2001f:52019)
  2. Andrea Höppner and Günter M. Ziegler. A census of flag-vectors of 4-polytopes. Polytopes—combinatorics and computation (Oberwolfach, 1997), 105–110, DMV Sem., 29, Birkhäuser, Basel, 2000. MR1785294 (2001e:52026) Günter M. Ziegler. Lectures on $0/1$-polytopes. Polytopes—combinatorics and computation (Oberwolfach, 1997), 1–41, DMV Sem., 29, Birkhäuser, Basel, 2000. MR1785291 (2001e:52017)
  3. M.M. Bayer, A.M. Bruening, and J.D. Stewart. A combinatorial study of multiplexes and ordinary polytopes. Geometric combinatorics (San Francisco, CA/Davis, CA, 2000). Discrete Comput. Geom. 27 (2002), no. 1, 49–63. MR1871688 (2002k:52012)
  4. Michael Joswig; Volker Kaibel; Marc E. Pfetsch; Günter M. Ziegler. Vertex-facet incidences of unbounded polyhedra. Adv. Geom. 1 (2001), no. 1, 23–36. MR1823950 (2002b:52015)
  5. Michael Joswig. Software integration and computer proofs. Mathematical software (Beijing, 2002), 15–28, World Sci. Publ., River Edge, NJ, 2002. MR1932601
  6. Christian Haase and Günter M. Ziegler. Examples and counterexamples for the Perles conjecture. Discrete Comput. Geom. 28 (2002), no. 1, 29–44. MR1904008 (2003e:52016)
  7. Volker Kaibel and Alexander Schwartz. On the complexity of polytope isomorphism problems. Graphs Combin. 19 (2003), no. 2, 215–230. MR1996205 (2004e:05125)
  8. Volker Kaibel and Marc E. Pfetsch. Some algorithmic problems in polytope theory. (English summary) Algebra, geometry, and software systems, 23–47, Springer, Berlin, 2003. MR2011752 (2004i:52012)
  9. Michael Joswig. Beneath-and-beyond revisited. Algebra, geometry, and software systems, 1–21, Springer, Berlin, 2003. MR2011751 (2004k:68169)
  10. Julian Pfeifle and Jörg Rambau. Computing triangulations using oriented matroids. Algebra, geometry, and software systems, 49–75, Springer, Berlin, 2003. MR2011753 (2004i:68233)
  11. Michael Joswig. Computing Invariants of Simplicial Manifolds. Preprint arXiv:math.AT/0401176.
  12. Julian Pfeifle and Günter M. Ziegler. On the monotone upper bound problem. Experiment. Math. 13 (2004), no. 1, 1–11. MR2065564 (2005f:52032)
  13. Bernd Sturmfels and Josephine Yu. Classification of six-point metrics. Electron. J. Combin. 11 (2004), no. 1, Research Paper 44, 16 pp. (electronic). MR2097310 (2005m:51016)
  14. Alexander Schwartz and Günter M. Ziegler. Construction techniques for cubical complexes, odd cubical 4-polytopes, and prescribed dual manifolds. (English summary) Experiment. Math. 13 (2004), no. 4, 385–413. MR2118264 (2007a:52015)
  15. Lior Pachter and Bernd Sturmfels (eds.). Algebraic statistics for computational biology, Cambridge Univ. Press, New York, 2005.
  16. Michael Joswig. Polytope propagation on graphs. Algebraic statistics for computational biology, 181–192, Cambridge Univ. Press, New York, 2005. MR2205871
  17. Steffen Schön and Hansjörg Kutterer. Using zonotopes for overestimation-free interval least-squares—some geodetic applications. (English summary) Reliab. Comput. 11 (2005), no. 2, 137–155. MR2147804 (2006c:65049)
  18. Peter Huggins, Bernd Sturmfels, Josephine Yu, and Debbie Yuster. The Hyperdeterminant and Triangulations of the 4-Cube, Math. Comp. 77 (2008), no. 263, 1653–1679. MR2398786
  19. James Cruickshank and Séamus Kelly. Rearrangement inequalities and the alternahedron. Discrete Comput. Geom. 35 (2006), no. 2, 241–254. MR2195053 (2006m:52019)
  20. Nicholas Eriksson, Stephen E. Fienberg, Alessandro Rinaldo, and Seth Sullivant. Polyhedral conditions for the nonexistence of the MLE for hierarchical log-linear models. J. Symbolic Comput. 41 (2006), no. 2, 222–233. MR2197157
  21. James Cruickshank and Séamus Kelly. Rearrangement inequalities and the alternahedron. Discrete Comput. Geom. 35 (2006), no. 2, 241–254. MR2195053 (2006m:52019)
  22. Matthias Beck and Serkan Hosten. Cyclotomic polytopes and growth series of cyclotomic lattices. Math. Res. Lett. 13 (2006), no. 4, 607–622. MR2250495 (2007h:52018)
  23. Robert Guralnick and David Perkinson. Permutation polytopes and indecomposable elements in permutation groups. J. Combin. Theory Ser. A 113 (2006), no. 7, 1243–1256. MR2259059 (2007h:05076)
  24. Michael Joswig; Marc E. Pfetsch. Computing optimal Morse matchings. SIAM J. Discrete Math. 20 (2006), no. 1, 11–25 (electronic). MR2257241 (2007h:90067)
  25. Andreas Paffenholz. New polytopes from products. J. Combin. Theory Ser. A 113 (2006), no. 7, 1396–1418. MR2259068 (2007m:52015)
  26. Seth Sullivant. Compressed polytopes and statistical disclosure limitation. Tohoku Math. J. (2) 58 (2006), no. 3, 433–445. MR2273279
  27. Michael Joswig and Nikolaus Witte. Products of foldable triangulations. Adv. Math. 210 (2007), no. 2, 769–796. MR2303239 (2008c:52017)
  28. Ulrich Derenthal. On a constant arising in Manin's conjecture for del Pezzo surfaces. Math. Res. Lett. 14 (2007), no. 3, 481–489. MR2318651
  29. Bernd Sturmfels, Jenia Tevelev and Josephine Yu. The Newton polytope of the implicit equation. Mosc. Math. J. 7 (2007), no. 2, 327–346, 351. MR2337885
  30. Michael Joswig and Thilo Rörig. Neighborly cubical polytopes and spheres. Israel J. Math. 159 (2007), 221–242.MR2342479
  31. Sven Herrmann and Michael Joswig. Bounds on the f-vectors of tight spans. Contrib. Discrete Math. 2 (2007), no. 2, 161–184 (electronic). MR2358269
  32. Eric Katz, Hannah Markwig, and Thomas Markwig. The j-invariant of a plane tropical cubic, J. Algebra 320 (2008), no. 10, 3832–3848. MR2457725
  33. Anton Leykin and Frank Sottile. Galois groups of Schubert problems via homotopy computation, Math. Comp. 78 (2009), no. 267, 1749–1765. MR2501073
  34. Matthias Beck, Christian Haase and Steven V. Sam. Grid graphs, Gorenstein polytopes and domino stackings, Graphs Combin. 25 (2009), no. 4, 409–426. MR2575592
  35. Victor Batyrev and Benjamin Nill. Multiples of lattice polytopes without interior lattice points. Moscow Math. J. 7 (2007), 195-207.
  36. Niko Beerenwinkel, Lior Pachter, and Bernd Sturmfels, Epistasis and Shapes of Fitness Landscapes, Statist. Sinica 17 (2007), no. 4, 1317–1342. MR2398598
  37. Weronika Buczynska and Jaroslav Wisniewski. On the geometry of binary symmetric models of phylogenetic trees, J. European Math. Soc. 9 (2007), 609-635 arXiv:math/0601357, MR2314109
  38. Geir Agnarsson and Walter Morris. On Minkowski Sums of Simplices, Ann. Comb. 13 (2009), no. 3, 271–287. MR2557038
  39. Christian Haase and Andreas Paffenholz. Groebner Bases for Transportation Polytopes. Preprint arXiv:math/0607194v1
  40. Raymond Hemmecke, Jason Morton, Anne Shiu, Bernd Sturmfels, and Oliver Wienand. Three Counterexamples on Semigraphoids. Preprint arXiv:math/0610451v1
  41. Joe Rusinko. Equivalence of Mirror Families Constructed from Toric Degenerations of Flag Varieties, Transform. Groups 13 (2008), no. 1, 173–194. MR2421321
  42. Peter Huggins, Lior Pachter, and Bernd Sturmfels. Towards the Human Genotope, Bull. Math. Biol. 69 (2007), no. 8, 2723–2735. MR2353852
  43. Brandon Ballinger, Grigoriy Blekherman, Henry Cohn, Noah Giansiracusa, Elizabeth Kelly, Achill Schuermann. Experimental study of energy-minimizing point configurations on spheres, Experiment. Math. 18 (2009), no. 3, 257–283. Only available as a preprint: arXiv:math/0611451v2
  44. Basudeb Datta and Nandini Nilakantan. Three dimensional pseudomanifolds on eight vertices, Int. J. Math. Math. Sci. 2008, 21 pp. Art. ID 254637
  45. Nico Düvelmeyer. General embedding problems and two-distance sets in Minkowski planes. Beiträge Algebra Geom. 49 (2008), no. 2, 549–598, MR2468075 (2009j:52007).
  46. Hadrien Mélot. Facet defining inequalities among graph invariants: the system GraPHedron. Discrete Appl. Math. 156 (2008), no. 10, 1875–1891. MR2432949 (2009f:05003)
  47. Armbruster, Michael; Christoph Helmberg; Marzena Fügenschuh; Alexander Martin. On the graph bisection cut polytope. SIAM J. Discrete Math. 22 (2008), no. 3, 1073–1098. MR2424838
  48. Fumei Lam; Alantha Newman. Traveling salesman path problems. Math. Program. 113 (2008), no. 1, Ser. A, 39–59. MR2367065 (2009b:90113)
  49. David Bremner, Mathieu Dutour Sikiric, and Achill Schuermann. Polyhedral representation conversion up to symmetries, Polyhedral computation, 45–71, CRM Proc. Lecture Notes, 48, Amer. Math. Soc., Providence, RI, 2009. Only available as a preprint: arXiv:math/0702239v2
  50. Jason Morton, Lior Pachter, Anne Shiu, Bernd Sturmfels, and Oliver Wienand. Convex Rank Tests and Semigraphoids, SIAM J. Discrete Math. 23 (2009), no. 3, 1117–1134. MR2538642
  51. Kord Eickmeyer and Ruriko Yoshida. Partitioning the Sample Space on Five Taxa for the Neighbor Joining Algorithm. Preprint arXiv:math/0703081v1
  52. Frederick A. Matsen, Elchanan Mossel and Mike Steel, Mixed-up trees: the structure of phylogenetic mixtures, Bull. Math. Biol. 70 (2008), no. 4, 1115–1139. MR2391182
  53. Bernd Sturmfels and Josephine Yu. Tropical Implicitization and Mixed Fiber Polytopes, Software for algebraic geometry, 111–131, IMA Vol. Math. Appl., 148, Springer, New York, 2008. Only available as a preprint: arXiv:0706.0564v1
  54. Michael Joswig, Bernd Sturmfels, and Josephine Yu. Affine Buildings and Tropical Convexity, Albanian J. Math. 1 (2007), no. 4, 187–211 . Only available as a preprint: arXiv:0706.1918v1
  55. Alexander Postnikov, David Speyer, and Lauren Williams. Matching polytopes, toric geometry, and the non-negative part of the Grassmannian. Preprint arXiv:0706.2501v2
  56. Stefan Forcey. Convex Hull Realizations of the Multiplihedra, Topology Appl. 156 (2008), no. 2, 326–347. MR2475119
  57. Nikolaus Witte. Constructing Combinatorial 4-Manifolds. Preprint arXiv:0707.1415v1
  58. Nikolaus Witte. Constructing Simplicial Branched Covers, Adv. Geom. 9 (2009), no. 3, 437–456. MR2537028
  59. Barbara Baumeister, Christian Haase, Benjamin Nill, and Andreas Paffenholz. On permutation polytopes, Adv. Math. 222 (2009), no. 2, 431–452. MR2538016
  60. Jesús A. De Loera, Edward D. Kim, Shmuel Onn, and Francisco Santos. Graphs of Transportation Polytopes, J. Combin. Theory Ser. A 116 (2009), no. 8, 1306–1325. MR2568801
  61. Thilo Rörig, Nikolaus Witte, and Günter M. Ziegler. Zonotopes With Large 2D Cuts, Discrete Comput. Geom. 42 (2009), no. 4, 527–541. MR2556453
  62. Kord Eickmeyer, Peter Huggins, Lior Pachter, and Ruriko Yoshida. On the optimality of the neighbor-joining algorithm. Preprint arXiv:0710.5142v1
  63. Lars Schewe. Non-Realizable Minimal Vertex Triangulations of Surfaces: Showing Non-Realizability using Oriented Matroids and Satisfiability Solvers. Preprint arXiv:0801.2582v1
  64. Bernd Sturmfels and Zhiqiang Xu. Sagbi Bases of Cox-Nagata Rings, J. Eur. Math. Soc. (JEMS) 12 (2010), no. 2, 429–459. MR2608947
  65. Edwin O'Shea and András Sebö. Alternatives for Testing Total Dual Integrality. Preprint arXiv:0803.2065v1
  66. Stefan Forcey. Quotients of the Multiplihedron as Categorified Associahedra, Homology, Homotopy Appl. 10 (2008), no. 2, 227–256. MR2475611
  67. Eric Katz, Hannah Markwig, and Thomas Markwig. The tropical $j$-invariant, LMS J. Comput. Math. 12 (2009), 275–294. MR2570928
  68. Sven Herrmann and Michael Joswig. Splitting Polytopes, Münster J. Math. 1 (2008), 109–141. MR2502496
  69. Frank H. Lutz, Thom Sulanke, and Ed Swartz. f-Vectors of 3-Manifolds, Electron. J. Combin. 16 (2009), no. 2, Special volume in honor of Anders Bjorner, Research Paper 13, 33 pp. MR2515776
  70. Satyan L. Devadoss and Stefan Forcey. Marked tubes and the graph multiplihedron, Algebr. Geom. Topol. 8 (2008), no. 4, 2081–2108. Only available as a preprint: arXiv:0807.4159v1
  71. Sven Herrmann, Anders Jensen, Michael Joswig, and Bernd Sturmfels. How to Draw Tropical Planes, Electron. J. Combin. 16 (2009), no. 2, Special volume in honor of Anders Bjorner, Research Paper 6, 26 pp. MR2515769
  72. Mathieu Dutour Sikiric; Graham Ellis. Wythoff polytopes and low-dimensional homology of Mathieu groups. J. Algebra 322 (2009), no. 11, 4143–4150. MR2556144
  73. Stephan, Rüdiger. Facets of the $(s,t)$-$p$-path polytope. Discrete Appl. Math. 157 (2009), no. 14, 3119–3132. Only available as a preprint: arXiv: math.OC/0606308
  74. Effenberger, Felix; Kühnel, Wolfgang. Hamiltonian submanifolds of regular polytopes. Discrete Comput. Geom. 43 (2010), no. 2, 242–262. MR2579694
  75. Dan Yasaki. Binary Hermitian forms over a cyclotomic field, J. Algebra 322 (2009), no. 11, 4132–4142. MR2556143
  76. Jose Martinez-Bernal, Edwin O'Shea, and Rafael H. Villarreal. Ehrhart clutters: Regularity and Max-Flow Min-Cut, Electron. J. Combin. 17 (2010), no. 1, Research Paper 52, 18 pp. MR2607338
  77. Xavier Allamigeon, Stéphane Gaubert, Eric Goubault. Computing the Extreme Points of Tropical Polyhedra (2009). Preprint arXiv:0904.3436
  78. Anne Shiu and Bernd Sturmfels. Siphons in chemical reaction networks, Bull. Math. Biol. 72 (2010), no. 6, 1448–1463. MR2671581
  79. Mathias Drton and Caroline J. Klivans. A Geometric Interpretation of the Characteristic Polynomial of Reflection Arrangements, Proc. Amer. Math. Soc. 138 (2010), no. 8, 2873–2887. MR2644900
  80. Edward D. Kim, Francisco Santos. An update on the Hirsch conjecture, Jahresber. Dtsch. Math.-Ver. 112 (2010), no. 2, 73–98. MR2681516
  81. Kord Eickmeyer, Ruriko Yoshida. The Geometry of the Neighbor-Joining Algorithm for Small Trees (2009). Preprint arXiv:0908.0098v1
  82. Stéphane Gaubert and Ricardo D. Katz. Minimal half-spaces and external representation of tropical polyhedra (2009). Preprint arXiv:0908.1586
  83. Sven Herrmann. Facets of Secondary Polytopes (2009). Preprint arXiv:0908.2537
  84. Jonathan Spreer and Wolfgang Kühnel. Combinatorial properties of the K3 surface: Simplicial blowups and slicings (2009). Preprint arXiv:0909.1453
  85. Ian Morrison, David Swinarski. Groebner techniques for low degree Hilbert stability (2009). Preprint arXiv:0910.2047
  86. Winfried Bruns and Bogdan Ichim. Normaliz: Algorithms for Affine Monoids and Rational Cones (2009). Preprint arXiv:0910.2845
  87. Bruno Benedetti, Frank H. Lutz. The dunce hat and a minimal non-extendably collapsible 3-ball (2009). Preprint arXiv:0912.3723
  88. Edward D. Kim, Francisco Santos. Companion to “An update on the Hirsch conjecture” (2009). Preprint arXiv:0912.4235
  89. Benjamin Lorenz. Classification of smooth lattice polytopes with few lattice points (2010). Preprint arXiv:1001.0514v1
  90. Jonathan Fine. A complete g-vector for convex polytopes (2010). Preprint arXiv:1001.1562v1
  91. Volker Kaibel. Basic Polyhedral Theory (2010). Preprint arXiv:1001.2161
  92. Maria Angelica Cueto and Frederick A. Matsen. Polyhedral geometry of Phylogenetic Rogue Taxa (2010). Preprint arXiv:1001.5241
  93. Alexander Engstrom, Patrik Noren. Ideals of Graph Homomorphisms (2010). Preprint arXiv:1002.4679
  94. Stavros Garoufalidis. Knots and tropical curves (2010). Preprint arXiv:1003.4436
  95. Tetsushi Matsui, Akihiro Higashitani, Yuuki Nagazawa et al. Roots of Ehrhart polynomials arising from graphs and posets (2010). Preprint arXiv:1003.5444
  96. Dusa McDuff. The topology of toric symplectic manifolds (2010). Preprint arXiv:1004.3227
  97. Felipe Rincon. Isotropical Linear Spaces and Valuated Delta-Matroids (2010). Preprint arXiv:1004.4950
  98. Stavros Garoufalidis. The degree of a q-holonomic sequence is a quadratic quasi-polynomial (2010). Preprint arXiv:1005.4580
  99. Francisco Santos. A counter-example to the Hirsch conjecture (2010) Preprint arXiv:1006.2814
  100. Benjamin Nill and Andreas Paffenholz. Examples of non-symmetric Kähler-Einstein toric Fano manifolds. Beitraege zur Algebra und Geometrie, 52(2), 2011, pp. 297-304 doi, arxiv:0905.2054
  101. Sandra Di Rocco, Christian Haase, Benjamin Nill and Andreas Paffenholz, Polyhedral Adjunction Theory, to appear in: Algebra and Number Theory arXiv:1105.2415
  102. Tristram Bogart, Christian Haase, Milena Hering, Benjamin Lorenz, Benjamin Nill, Andreas Paffenholz, Francisco Santos, and Hal Schenck, Few smooth d-polytopes with N lattice points, arXiv:1010.3887
  103. Richard Bödi, Katrin Herr, and Michael Joswig, Algorithms for Highly Symmetric Linear and Integer Programs, arXiv:1012.4941
  104. Barbara Baumeister, Christian Haase, Benjamin Nill, and Andreas Paffenholz, Permutation Polytopes of Cyclic Groups, extended abstract, Proceedings of FPSAC 2012, DMTCS, pp. 421-432
  105. Barbara Baumeister, Christian Haase, Benjamin Nill, and Andreas Paffenholz, Permutation Polytopes of Cyclic Groups, arXiv:1109.0191
  106. Michael Joswig and Andreas Paffenholz, Defect Polytopes and Counter-Examples With polymake, extended abstract, Issac 2011, arXiv:1105.5027
  107. Barbara Baumeister, Christian Haase, Benjamin Nill, and Andreas Paffenholz, Polytopes associated to Dihedral Groups, Ars Math. Cont., 7(1), 2014, pp. 30-38
  108. Benjamin Assarf, Michael Joswig, and Andreas Paffenholz, Smooth Fano Polytopes With Many Vertices, arXiv:1209.3186
  109. Benjamin Lorenz and Benjamin Nill, On smooth Gorenstein polytopes, arXiv:1303.2138
  110. Olivia Beckwith and Matthew Grimm and Jenya Soprunova and Bradley Weaver, Minkowski length of 3D lattice polytopes, Discrete Comput. Geom. 48 (2012), no. 4, 1137–1158.
  111. Matthias Henze, On counterexamples to a conjecture of Wills and Ehrhart polynomials whose roots have equal real parts, Electron. J. Combin. 21 (2014), no. 1, Paper 1.28, 12 pp.
  112. Simon Hampe, a-tint: a polymake extension for algorithmic tropical intersection theory, European J. Combin. 36 (2014), 579–607.
  113. Carsten Lange, Minkowski decomposition of associahedra and related combinatorics, Discrete Comput. Geom. 50 (2013), no. 4, 903–939.
  114. Arnau Padrol, Many neighborly polytopes and oriented matroids, Discrete Comput. Geom. 50 (2013), no. 4, 865–902.
  115. Andreas Paffenholz, Finiteness of the polyhedral Q-codegree spectrum, to appear in: Proc. AMS, 2014.
  116. Andreas Paffenholz Faces of Birkhoff Polytopes, preprint, TU Darmstadt, April 2013, 29 pages. arXiv:1304.3948
  117. Christian Haase, Lindsay Piechnik, Andreas Paffenholz and Francisco Santos, Existence of regular unimodular triangulations — Positive Results, preprint, TU Darmstadt, May 2014, 82 pages, arXiv:1405.1687
  • publications.txt
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