The Book

J. A. De Loera, J. Rambau, F. Santos Triangulations: Structures for Algorithms and Applications, 539 pp. Algorithms and Computation in Mathematics, Vol. 25, Springer-Verlag. ISBN: 978-3-642-12970-4

Research papers by Francisco Santos

Links to my list of papers in MATHSCINET and Zentralblatt MATH.

Below is the list of full references, in reverse chronological order. To get a paper, click on the title or on the link to the appropriate page of arXiv.org. Where available, a link to the journal issue or journal home page for published papers is included.

Needless--but probably mandatory--to say, copyright of published papers is held by the publisher.

Preprints or submitted papers:

• Benjamin Matschke, Francisco Santos, Christophe Weibel, The width of 5-dimensional prismatoids
  Preprint, February 2012, 28 pages.
  arXiv:1202.4701


• Francisco Santos, Some acyclic systems of permutations are not realizable by triangulations of a product of simplices
  Preprint, January 2012, 12 pages.
  arXiv:1201.0529


• Cesar Ceballos, Francisco Santos, Günter M. Ziegler, Many non-equivalent realizations of the associahedron
  Preprint, September 2011, 28 pages.
  arXiv:1109.5544


• Tristram Bogart, Christian Haase, Milena Hering, Benjamin Lorenz, Benjamin Nill, Andreas Paffenholz, Francisco Santos, Hal Schenck, Few smooth d-polytopes with N lattice points
  Preprint, October 2010, 19 pages.
  arXiv:1010.3887
  

Papers accepted for publication:

• Oswin Aichholzer, Thomas Hackl, Michael Hoffmann, Clemens Huemer, Attila Pór, Francisco Santos, Bettina Speckmann, Birgit Vogtenhuber, Maximizing Maximal Angles for Plane Straight-Line Graphs.
  Accepted in Computational Geometry: Theory and Applications.
  DOI: 10.1016/j.comgeo.2012.03.002
  This is the final version of this paper.


• Francisco Santos, A counter-example to the Hirsch conjecture
  Preprint, June 2010, 27 pages.
  arXiv:1006.2814
  Annals of Math. (2), to appear. (Published online November 2011)


• Julian Pfeifle, Vincent Pilaud, Francisco Santos, Polytopality and Cartesian products of graphs
  Preprint, September 2010, 21 pages.
  arXiv:1009.1499
  Accepted in Israel J. Math.

Published papers in (more or less) reverse chronological order:

• Francisco Santos, Tamon Stephen, Hugh Thomas, Embedding a pair of graphs in a surface, and the width of 4-dimensional prismatoids.
  arXiv:1104.2630
  Discrete Comput. Geom. 47:3 (2012), 569-576. DOI: 10.1007/s00454-011-9361-9


• Vincent Pilaud, Francisco Santos, The brick polytope of a sorting network.
  arXiv:1103.2731
  European J. Combin. 33:4 (2012), 632-662.

• P. Sabariego and F. Santos, On the number of facets of three-dimensional Dirichlet stereohedra IV: Quarter cubic groups.
  arXiv:0708.2114
  Contributions to Algebra and Geometry 52:2 (2011), 237-263. DOI: 10.1007/s13366-011-0010-5
  See also part I, part II and part III in this series.

• C. Cortés, C. I. Grima, F. Hurtado, A. Márquez, F. Santos, J. Valenzuela, Transforming triangulations on non planar surfaces.
  arXiv:math.MG/0311228
  SIAM J. Discrete Math. 24:3 (2010), 821-840.
  DOI: 10.1137/070697987


• Francisco Santos, Sobre un contraejemplo a la Conjetura de Hirsch,
  arXiv:1007.3283
  La Gaceta de la RSME, Vol. 13 (2010), Num. 3, 525-538.
  This paper was translated into German by Julian Pfeifle, and has appeared in Mitteilungen der DMV, Vol. 18-4 (Winter 2010), 214-220.


• E.D. Kim and F. Santos, An update on the Hirsch conjecture.
  arXiv:0907.1186
  Jahresbericht der Deutschen Mathematiker-Vereinigung, Volume 112(2) (June 2010), 73-98.
  DOI: 10.1365/s13291-010-0001-8.
  An unpublished "companion paper" with remarks, additional content and proofs of some of the results in this survey can be found as arXiv:0912.4235.

• J. A. de Loera, E. D. Kim, S. Onn, and F. Santos, Graphs of transportation polytopes,
  arXiv:0709.2189
  J. Combin. Theory Ser. A, 116(8), November 2009, 1306-1325.


• P. Sabariego and F. Santos, Triple-loop networks with arbitrarily many minimum distance diagrams.
  arXiv:0705.3631
  Discrete Mathematics, 309(6), April 2009, 1672-1684.


• V. Pilaud and F. Santos, Multi-triangulations as complexes of star polygon.
  arXiv:0706.3121
  Discrete Comput. Geom., 41(2), March 2009, 284-317.

• P. Sabariego and F. Santos, On the number of facets of three-dimensional Dirichlet stereohedra III: Full cubic groups.
  http://arxiv.org/abs/math.CO/0608039
  Discrete Comput. Geom., 40(2) (2008), 159-189.
  See also part I, part II and part IV in this series.


• Christian Haase, Benjamin Nill, Andreas Paffenholz, and Francisco Santos, Lattice points in Minkowski sums,
  arXiv:0711.4393
  Electron J. Combin., 15 (2008), no. 1, Note 11, 5 pp.


• G. Rote, F. Santos, and I. Streinu, Pseudo-triangulations - a survey.
  http://arxiv.org/abs/math.CO/0612672
  Surveys on Discrete and Computational Geometry: Twenty Years Later, Edited by J. E. Goodman, J. Pach, and R. Pollack, Contemporary Mathematics 453, AMS, 2008. ISBN-13: 978-0-8218-4239-3


• O. Aichholzer, D. Orden, F. Santos, and B. Speckmann, On the Number of Pseudo-Triangulations of Certain Point Sets.
  http://arxiv.org/abs/math.CO/0601747
  J. Combin. Theory Ser. A, 115 (2008) 254-278.

• Oswin Aichholzer, Thomas Hackl, Michael Hoffmann, Clemens Huemer, Attila Pór, Francisco Santos, Bettina Speckmann, Birgit Vogtenhuber, Maximizing Maximal Angles for Plane Straight-Line Graphs.
  arxiv:0705.3820
  In, Algorithms and Data Structures 10th International Workshop, WADS 2007, Halifax, Canada, August 15-17, 2007, Frank Dehne, Jörg-Rüdiger Sack, Norbert Zeh (Eds.), Lecture Notes in Computer Science 4619, Springer-Verlag, 2007, pp. 458-469.
  Final version of this paper is here.
  


• C. A. Athanasiadis, V. V. Batyrev, D. I. Dais, M. Henk, F. Santos, (Editors).
  Algebraic and Geometric Combinatorics.
  Contemporary Maths 423, AMS, Providence, 2007. ISBN-13: 978-0-8218-4080-1.


• D. Orden, F. Santos, B. Servatius, H. Servatius, Combinatorial Pseudo-Triangulations.
  http://arxiv.org/abs/math.CO/0307370
  Discrete Mathematics, 307 (2007), 554-566.


• F. Santos, A. Schürmann, F. Vallentin, Lattice Delone simplices with exponential volume.
  http://arxiv.org/abs/math.CO/0507119
  European J. Combin. 28:3 (2007), 801-806.


• F. Santos, Geometric bistellar flips. The setting, the context and a construction.
  http://arxiv.org/abs/math.CO/0601746
  In Proceedings of the International Congress of Mathematicians, Madrid, August 22-30, 2006 (Marta Sanz-Solé, Javier Soria, Juan Luis Varona, Joan Verdera, eds.), European Mathematical Society, 2006, Vol III, pp. 931-962. ISBN 978-3-03719-022-7

• D. Bochis and F. Santos, On the number of facets of three-dimensional Dirichlet stereohedra II: Non-cubic groups.
  http://arxiv.org/abs/math.CO/0204231
  Beiträge Algebra Geom., 47:1 (2006), 89-120.
  See also part I, part III and part IV in this series.

• M. Develin, F. Santos, and B. Sturmfels, On the tropical rank of a matrix.
  http://arxiv.org/abs/math.CO/0312114
  In Combinatorial and Computational Geometry (J. E. Goodman, J. Pach and E. Welzl, eds), MSRI Publications 52, Cambridge University Press, 2005, pp. 213-242. ISBN-10: 0521848628

• F. Santos, Non-connected toric Hilbert schemes.
  http://arxiv.org/abs/math.CO/0204044.
  Mathematische Annalen, 332:3 (2005), 645-665. DOI:10.1007/s00208-005-0643-5

• F. Santos, The Cayley Trick and triangulations of products of simplices.
  http://arxiv.org/abs/math.CO/0312069
  In Integer Points in Polyhedra -- Geometry, Number Theory, Algebra, Optimization (proceedings of the AMS-IMS-SIAM Summer Research Conference) edited by A. Barvinok, M. Beck, C. Haase, B. Reznick, and V. Welker, Contemporary Mathematics 374, American Mathematical Society, 2005, pp. 151-177. ISBN 0-8218-3459-2.
• R. Haas, D. Orden, G. Rote, F. Santos, B. Servatius, H. Servatius, D. Souvaine, I. Streinu and W. Whiteley, Planar Minimally Rigid Graphs and Pseudo-Triangulations http://arxiv.org/abs/math.CO/0307347
  Computational Geometry: theory and Applications 31:1-2 (May 2005), 31-61.
  A preliminary shorter version appeared in the Proceedings of the nineteenth annual symposium on Computational geometry, ACM Press, New York, 2003, pp. 154-163.
  

• L. Bowen, J. A. de Loera, M. Develin, F. Santos, The Gromov norm of the product of two surfaces.
  http://arxiv.org/abs/math.MG/0407176
  Topology 44:2 (March 2005), 321-339. An erratum has appeared in 47:6 (November 2008), 471-472.

• D. Orden and F. Santos, The polytope of non-crossing graphs on a planar point set.
  http://arxiv.org/abs/math.CO/0302126
  Discrete Comput. Geom. 33:2 (2005), 275-305.

• D. Orden, G. Rote, F. Santos, B. Servatius, H. Servatius, W. Whiteley, Non-crossing frameworks with non-crossing reciprocals.
  http://arxiv.org/abs/math.MG/0309156
  Discrete Comput. Geom., 32:4 (2004), 567-600.

• D. Orden, F. Santos, Asymptotically efficient triangulations of the d-cube.
  http://arxiv.org/abs/math.CO/0204157
  Discrete Comput. Geom., 30:4 (2003), 509-528.
  An extended abstract appeared in "Comb01, Euroconference on Combinatorics, Graph Theory and Applications" Electronic Notes in Discrete Mathematics 10 (2001), 212-215.

• G. Rote, F. Santos and I. Streinu, Expansive motions and the Polytope of Pointed Pseudo-Triangulations.
  http://arxiv.org/abs/math.CO/0206027
  In Discrete and Computational Geometry -- The Goodman-Pollack Festschrift (B. Aronov, S. Basu, J. Pach, M. Sharir, eds), Algorithms and Combinatorics 25, Springer Verlag, Berlin, June 2003, pp. 699-736.

• F. Santos and B. Sturmfels, Higher Lawrence configurations.
  http://arxiv.org/abs/math.CO/0209326
  J. Combin. Theory, Ser. A. 103:1 (2003), 151-164.

• F. Santos and R. Seidel, A better upper bound on the number of triangulations of a planar point set.
  http://arxiv.org/abs/math.CO/0204045
  J. Combin. Theory Ser. A, 102:1 (2003), 186-193.

• F. Santos and B. Sturmfels, Alexander duality in subdivisions of Lawrence polytopes.
  http://arxiv.org/abs/math.CO/0202104
  Adv. Geom., 3:2 (2003), 177-189. DOI:10.1515/advg.2003.012

• F. Santos, Triangulations of oriented matroids (282K, *.ps.gz).
  Mem. Amer. Math. Soc., volume 156, number 741, American Mathematical Society, 2002.

• C. A. Athanasiadis and F. Santos, On the topology of the Baues poset of polyhedral subdivisions (79K, *.ps.gz).
  Topology, 41 (2002) no.3, 423-433.

• M. Azaola and F. Santos, The number of triangulations of the cyclic polytope C(n,n-4) (119K, *.ps.gz).
  Discrete Comput. Geom., 27 (2002), 29-48.

• C. A. Athanasiadis and F. Santos, Monotone paths on zonotopes and oriented matroids (107K, *.ps.gz).
  Canad. J. Math., 53 (2001), no. 6, 1121-1140.

• F. Santos, On the refinements of a polyhedral subdivision (139K, *.ps.gz). The journal version contains a minor error in the proof of Theorem 2.8. This is the erratum file (February 2002).
  Collect. Math. 52:3 (2001), 231-256.

• D. Randall, G. Rote, F. Santos and J. Snoeyink, Counting triangulations and pseudo-triangulations of wheels (463K, *.ps).
  This is the long version (8 pages) of the short one (4 pages) appeared in Proceedings 13th Canad. Conf. Comput. Geom., 2001, pp. 149-152.

• J. A. de Loera, F. Takeuchi and F. Santos, Extremal properties for dissections of convex 3-polytopes (248K, *.ps.gz).
  SIAM J. Discrete Math. 14:2 (2001), 143-161.

• F. Santos, Realizable but not strongly Euclidean oriented matroids (100K, *.ps.gz).
  In "Special issue on Combinatorial Geometries" (R. Cordovil and M. Las Vergnas, eds.),
  European J. Combin 22:5 (2001), 767-776.

• D. Bochis and F. Santos, On the number of facets of three-dimensional Dirichlet stereohedra I: groups with reflections (163K, *.ps.gz).
  Discrete Comput. Geom. 25:3 (2001), 419-444.
  See also part II, part III and part IV in this series.

• B. Huber, J. Rambau and F. Santos, The Cayley trick, lifting subdivisions and the Bohne-Dress Theorem on zonotopal tilings (64K, *.ps.gz).
  J. Eur. Math. Soc. (JEMS) 2:2 (2000), 179-198.

• F. Santos, A point configuration whose space of triangulations is disconnected (196K, *.ps.gz).
  J. Amer. Math. Soc. 13:3 (2000), 611-637.

• M. Azaola and F. Santos, The graph of triangulations of a point configuration with d+4 vertices is 3-connected (215K, *.ps.gz).
  Discrete Comput. Geom. 23:4 (2000), 489-536.
  

  See also the related paper: M. Azaola, The Baues conjecture in corank 3 (175K, *.ps.gz). Topology, 41:1, (2002) 183-209.

• C. A. Athanasiadis, J. A. de Loera, V. Reiner and F. Santos, Fiber polytopes for the projections between cyclic polytopes (156K, *.ps.gz).
  In "Special issue on Combinatorics of convex polytopes" (K. Fukuda and G. M. Ziegler, eds.),
  European J. Combin. 21:1 (2000), 19-47.

• J. Rambau and F. Santos, The generalized Baues problem for cyclic polytopes I (74K, *.ps.gz).
  In "Special issue on Combinatorics of convex polytopes" (K. Fukuda and G. M. Ziegler, eds.),
  European J. Combin. 21:1 (2000), 65-83.
  Also available an extended version of Section 5.

• F. Santos, Triangulations with very few geometric bistellar neighbors (142K, *.ps.gz).
  Discrete Comput. Geom. 23:1 (2000), 15-33.

• C. A. Athanasiadis, J. Rambau and F. Santos, The generalized Baues problem for cyclic polytopes II (54K, *.ps.gz).
  In "Geometric combinatorics (Kotor, 1998)".
  Publ. Inst. Math. (Beograd) (N.S.) 66(80) (1999), 3-15.

• Christian Icking, Rolf Klein, Ngoc-Minh Le, Lihong Ma, Francisco Santos, On Bisectors for Convex Distance Functions in 3-Space (194K, *.ps.gz),
  Proceedings 11th Canad. Conf. Comput. Geom., 1999.

• J. A. de Loera, F. Santos, J. Urrutia, The number of geometric bistellar neighbors of a triangulation (88K, *.ps.gz).
  Discrete Comput. Geom. 21:1 (1999), 131-142.

• F. Santos, Construction of real algebraic plane nodal curves with given topology and optimal degree, I (466K, *.ps.gz).
  Rev. Mat. Univ. Complut. Madrid, 10 (1997) 291-310.

• J. A. de Loera, S. Hosten, F. Santos, B. Sturmfels, The polytope of all triangulations of a point configuration (90K, *.ps.gz).
  Doc. Math. J. DMV. 1 (1996) 103-119.

• F. Santos, On Delaunay oriented matroids for convex distance functions (490K, *.ps.gz).
  Discrete Comput. Geom. 16 (1996) 2, 197-210.

• F. Santos, Inscribing a symmetric body in an ellipse (36K, *.ps.gz).
  Inform. Process. Lett. 59 4 (1996) 175-178.

• M. J. González-López, T. Recio, F. Santos, Parametrization of semialgebraic sets (53K, *.ps.gz).
  Math. Comput. Simulat., 42 (1996) 353-362.

• J. A. de Loera and F. Santos, An effective version of Pólya's theorem on positive definite forms (146K, *.ps.gz).
  J. Pure Appl. Algebra, 108 (1996) 231-240.
  A correction of errors has appeared in J. Pure Appl. Algebra, 155 (2001) 309-310.

• F. Santos, Construction of singular algebraic plane nodal curves with given topology (574K, *.ps.gz).
  In Real Analytic and Algebraic Geometry. Proccedings of the international conference, Trento, Italy, September 21--25, 1992. Walter De Gruyter Publishers, Berlin 1995, pp. 213--228.

• A. G. Corbalán, M. Mazón, T. Recio, F. Santos, On the topological shape of planar Voronoi diagrams (470K, *.ps.gz).
  Proceedings of the 9th Annual Symposium on Computational Geometry, Association for Computing Machinery Inc., New York, 1993, 109-115.