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)
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.
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.
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
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
Sven Herrmann, Michael Joswig, and Marc E. Pfetsch. Computing the bounded subcomplex of an unbounded polyhedron. arXiv:1006.2767
Michael Joswig and Andreas Paffenholz. Defect Polytopes and Counter-Examples With polymake. arXiv:1105.0527
Michael Joswig; Günter M. Ziegler. Neighborly cubical polytopes. The Branko Grünbaum birthday issue. Discrete Comput. Geom. 24 (2000), no. 2-3, 325–344. MR1758054 (2001f:52019)
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)
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)
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)
Michael Joswig. Software integration and computer proofs. Mathematical software (Beijing, 2002), 15–28, World Sci. Publ., River Edge, NJ, 2002. MR1932601
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)
Volker Kaibel and Alexander Schwartz. On the complexity of polytope isomorphism problems. Graphs Combin. 19 (2003), no. 2, 215–230. MR1996205 (2004e:05125)
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)
Michael Joswig. Beneath-and-beyond revisited. Algebra, geometry, and software systems, 1–21, Springer, Berlin, 2003. MR2011751 (2004k:68169)
Julian Pfeifle and Jörg Rambau. Computing triangulations using oriented matroids. Algebra, geometry, and software systems, 49–75, Springer, Berlin, 2003. MR2011753 (2004i:68233)
Michael Joswig. Computing Invariants of Simplicial Manifolds. Preprint arXiv:math.AT/0401176.
Julian Pfeifle and Günter M. Ziegler. On the monotone upper bound problem. Experiment. Math. 13 (2004), no. 1, 1–11. MR2065564 (2005f:52032)
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)
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)
Lior Pachter and Bernd Sturmfels (eds.). Algebraic statistics for computational biology, Cambridge Univ. Press, New York, 2005.
Michael Joswig. Polytope propagation on graphs. Algebraic statistics for computational biology, 181–192, Cambridge Univ. Press, New York, 2005. MR2205871
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)
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
James Cruickshank and Séamus Kelly. Rearrangement inequalities and the alternahedron. Discrete Comput. Geom. 35 (2006), no. 2, 241–254. MR2195053 (2006m:52019)
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
James Cruickshank and Séamus Kelly. Rearrangement inequalities and the alternahedron. Discrete Comput. Geom. 35 (2006), no. 2, 241–254. MR2195053 (2006m:52019)
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)
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)
Michael Joswig; Marc E. Pfetsch. Computing optimal Morse matchings. SIAM J. Discrete Math. 20 (2006), no. 1, 11–25 (electronic). MR2257241 (2007h:90067)
Andreas Paffenholz. New polytopes from products. J. Combin. Theory Ser. A 113 (2006), no. 7, 1396–1418. MR2259068 (2007m:52015)
Seth Sullivant. Compressed polytopes and statistical disclosure limitation. Tohoku Math. J. (2) 58 (2006), no. 3, 433–445. MR2273279
Michael Joswig and Nikolaus Witte. Products of foldable triangulations. Adv. Math. 210 (2007), no. 2, 769–796. MR2303239 (2008c:52017)
Ulrich Derenthal. On a constant arising in Manin's conjecture for del Pezzo surfaces. Math. Res. Lett. 14 (2007), no. 3, 481–489. MR2318651
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
Michael Joswig and Thilo Rörig. Neighborly cubical polytopes and spheres. Israel J. Math. 159 (2007), 221–242.MR2342479
Sven Herrmann and Michael Joswig. Bounds on the f-vectors of tight spans. Contrib. Discrete Math. 2 (2007), no. 2, 161–184 (electronic). MR2358269
Eric Katz, Hannah Markwig, and Thomas Markwig. The j-invariant of a plane tropical cubic, J. Algebra 320 (2008), no. 10, 3832–3848. MR2457725
Anton Leykin and Frank Sottile. Galois groups of Schubert problems via homotopy computation, Math. Comp. 78 (2009), no. 267, 1749–1765. MR2501073
Matthias Beck, Christian Haase and Steven V. Sam. Grid graphs, Gorenstein polytopes and domino stackings, Graphs Combin. 25 (2009), no. 4, 409–426. MR2575592
Victor Batyrev and Benjamin Nill. Multiples of lattice polytopes without interior lattice points. Moscow Math. J. 7 (2007), 195-207.
Niko Beerenwinkel, Lior Pachter, and Bernd Sturmfels, Epistasis and Shapes of Fitness Landscapes, Statist. Sinica 17 (2007), no. 4, 1317–1342. MR2398598
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
Jason Morton, Lior Pachter, Anne Shiu, Bernd Sturmfels, and Oliver Wienand. Geometry of rank tests. Preprint arXiv:math/0605173v2
Geir Agnarsson and Walter Morris. On Minkowski Sums of Simplices, Ann. Comb. 13 (2009), no. 3, 271–287. MR2557038
Christian Haase and Andreas Paffenholz. Groebner Bases for Transportation Polytopes. Preprint arXiv:math/0607194v1
Raymond Hemmecke, Jason Morton, Anne Shiu, Bernd Sturmfels, and Oliver Wienand. Three Counterexamples on Semigraphoids. Preprint arXiv:math/0610451v1
Joe Rusinko. Equivalence of Mirror Families Constructed from Toric Degenerations of Flag Varieties, Transform. Groups 13 (2008), no. 1, 173–194. MR2421321
Peter Huggins, Lior Pachter, and Bernd Sturmfels. Towards the Human Genotope, Bull. Math. Biol. 69 (2007), no. 8, 2723–2735. MR2353852
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
Basudeb Datta and Nandini Nilakantan. Three dimensional pseudomanifolds on eight vertices, Int. J. Math. Math. Sci. 2008, 21 pp. Art. ID 254637
Nico Düvelmeyer. General embedding problems and two-distance sets in Minkowski planes. Beiträge Algebra Geom. 49 (2008), no. 2, 549–598, MR2468075 (2009j:52007).
Hadrien Mélot. Facet defining inequalities among graph invariants: the system GraPHedron. Discrete Appl. Math. 156 (2008), no. 10, 1875–1891. MR2432949 (2009f:05003)
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
Fumei Lam; Alantha Newman. Traveling salesman path problems. Math. Program. 113 (2008), no. 1, Ser. A, 39–59. MR2367065 (2009b:90113)
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
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
Kord Eickmeyer and Ruriko Yoshida. Partitioning the Sample Space on Five Taxa for the Neighbor Joining Algorithm. Preprint arXiv:math/0703081v1
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
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
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
Alexander Postnikov, David Speyer, and Lauren Williams. Matching polytopes, toric geometry, and the non-negative part of the Grassmannian. Preprint arXiv:0706.2501v2
Stefan Forcey. Convex Hull Realizations of the Multiplihedra, Topology Appl. 156 (2008), no. 2, 326–347. MR2475119
Nikolaus Witte. Constructing Combinatorial 4-Manifolds. Preprint arXiv:0707.1415v1
Nikolaus Witte. Constructing Simplicial Branched Covers, Adv. Geom. 9 (2009), no. 3, 437–456. MR2537028
Barbara Baumeister, Christian Haase, Benjamin Nill, and Andreas Paffenholz. On permutation polytopes, Adv. Math. 222 (2009), no. 2, 431–452. MR2538016
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
Thilo Rörig, Nikolaus Witte, and Günter M. Ziegler. Zonotopes With Large 2D Cuts, Discrete Comput. Geom. 42 (2009), no. 4, 527–541. MR2556453
Kord Eickmeyer, Peter Huggins, Lior Pachter, and Ruriko Yoshida. On the optimality of the neighbor-joining algorithm. Preprint arXiv:0710.5142v1
Lars Schewe. Non-Realizable Minimal Vertex Triangulations of Surfaces: Showing Non-Realizability using Oriented Matroids and Satisfiability Solvers. Preprint arXiv:0801.2582v1
Bernd Sturmfels and Zhiqiang Xu. Sagbi Bases of Cox-Nagata Rings, J. Eur. Math. Soc. (JEMS) 12 (2010), no. 2, 429–459. MR2608947
Edwin O'Shea and András Sebö. Alternatives for Testing Total Dual Integrality. Preprint arXiv:0803.2065v1
Stefan Forcey. Quotients of the Multiplihedron as Categorified Associahedra, Homology, Homotopy Appl. 10 (2008), no. 2, 227–256. MR2475611
Eric Katz, Hannah Markwig, and Thomas Markwig. The tropical $j$-invariant, LMS J. Comput. Math. 12 (2009), 275–294. MR2570928
Sven Herrmann and Michael Joswig. Splitting Polytopes, Münster J. Math. 1 (2008), 109–141. MR2502496
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
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
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
Mathieu Dutour Sikiric; Graham Ellis. Wythoff polytopes and low-dimensional homology of Mathieu groups. J. Algebra 322 (2009), no. 11, 4143–4150. MR2556144
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
Effenberger, Felix; Kühnel, Wolfgang. Hamiltonian submanifolds of regular polytopes. Discrete Comput. Geom. 43 (2010), no. 2, 242–262. MR2579694
Dan Yasaki. Binary Hermitian forms over a cyclotomic field, J. Algebra 322 (2009), no. 11, 4132–4142. MR2556143
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
Xavier Allamigeon, Stéphane Gaubert, Eric Goubault. Computing the Extreme Points of Tropical Polyhedra (2009). Preprint arXiv:0904.3436
Anne Shiu and Bernd Sturmfels. Siphons in chemical reaction networks, Bull. Math. Biol. 72 (2010), no. 6, 1448–1463. MR2671581
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
Edward D. Kim, Francisco Santos. An update on the Hirsch conjecture, Jahresber. Dtsch. Math.-Ver. 112 (2010), no. 2, 73–98. MR2681516
Kord Eickmeyer, Ruriko Yoshida. The Geometry of the Neighbor-Joining Algorithm for Small Trees (2009). Preprint arXiv:0908.0098v1
Stéphane Gaubert and Ricardo D. Katz. Minimal half-spaces and external representation of tropical polyhedra (2009). Preprint arXiv:0908.1586
Sven Herrmann. Facets of Secondary Polytopes (2009). Preprint arXiv:0908.2537
Jonathan Spreer and Wolfgang Kühnel. Combinatorial properties of the K3 surface: Simplicial blowups and slicings (2009). Preprint arXiv:0909.1453
Ian Morrison, David Swinarski. Groebner techniques for low degree Hilbert stability (2009). Preprint arXiv:0910.2047
Winfried Bruns and Bogdan Ichim. Normaliz: Algorithms for Affine Monoids and Rational Cones (2009). Preprint arXiv:0910.2845
Bruno Benedetti, Frank H. Lutz. The dunce hat and a minimal non-extendably collapsible 3-ball (2009). Preprint arXiv:0912.3723
Edward D. Kim, Francisco Santos. Companion to “An update on the Hirsch conjecture” (2009). Preprint arXiv:0912.4235
Benjamin Lorenz. Classification of smooth lattice polytopes with few lattice points (2010). Preprint arXiv:1001.0514v1
Jonathan Fine. A complete g-vector for convex polytopes (2010). Preprint arXiv:1001.1562v1
Volker Kaibel. Basic Polyhedral Theory (2010). Preprint arXiv:1001.2161
Maria Angelica Cueto and Frederick A. Matsen. Polyhedral geometry of Phylogenetic Rogue Taxa (2010). Preprint arXiv:1001.5241
Alexander Engstrom, Patrik Noren. Ideals of Graph Homomorphisms (2010). Preprint arXiv:1002.4679
Stavros Garoufalidis. Knots and tropical curves (2010). Preprint arXiv:1003.4436
Tetsushi Matsui, Akihiro Higashitani, Yuuki Nagazawa et al. Roots of Ehrhart polynomials arising from graphs and posets (2010). Preprint arXiv:1003.5444
Dusa McDuff. The topology of toric symplectic manifolds (2010). Preprint arXiv:1004.3227
Felipe Rincon. Isotropical Linear Spaces and Valuated Delta-Matroids (2010). Preprint arXiv:1004.4950
Stavros Garoufalidis. The degree of a q-holonomic sequence is a quadratic quasi-polynomial (2010). Preprint arXiv:1005.4580
Francisco Santos. A counter-example to the Hirsch conjecture (2010) Preprint arXiv:1006.2814
Benjamin Nill and Andreas Paffenholz. Examples of non-symmetric Kähler-Einstein toric Fano manifolds. Beitraege zur Algebra und Geometrie, 2011, to appear. doi, arxiv:0905.2054
Sandra Di Rocco, Christian Haase, Benjamin Nill and Andreas Paffenholz, Polyhedral Adjunction Theory. arXiv:1105.2415
Richard Bödi, Katrin Herr, and Michael Joswig, Algorithms for Highly Symmetric Linear and Integer Programs, arXiv:1012.4941
