DR. Silvia fernandez

Classes Fall 2012

Math 150A. Calculus 1. MWR 2:00-3:25 pm. Chaparral Hall CR 5123.

Final Exam. Saturday, May 11, 11:30am-1:30pm. 

Math 661B. Advanced Topics in Discrete Mathematics. MWR 3:30-4:45 pm. Chaparral Hall CR 5123.

Publications

• B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, P. Ramos, and G. Salazar. The 2-page crossing number of Kn. Submitted. arXiv:1206.5669.
• B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, P. Ramos, and G. Salazar. The 2-page crossing number of Kn (Extended Abstract). Proceedings of the ACM Symposium on Computational Geometry, June 17–20, 2012, Chapel Hill, North Carolina, USA. (2012) 397-403.
• B. M. Ábrego, S. Fernández-Merchant, and G. Salazar. The rectilinear crossing number of Kn: Closing in (or are we?). In Thirty essays in geometric graph theory, J. Pach (Ed), Springer (2013), XVI, 504 p.
• B. M. Ábrego, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, H. Meijer, V. Sacristán, M. Saumell. Proximity graphs inside large weighted graphs. Networks (2013) doi: 10.1002/net.21464.
• B. M. Ábrego, S. Fernández-Merchant, and B. Llano. An inequality for Kruskal-Macaulay Functions, Journal of Integer Sequences, 14 (2011) Article 11.7.4.
• B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, J. Leaños, and G. Salazar. There is a unique crossing-minimal rectilinear drawing of K18. Electronic Notes in Discrete Mathematics 38 (2011) 547-552.
• B. M. Ábrego, M. Cetina, S. Fernández-Merchant, J. Leaños, and G. Salazar. On (<=k)-edges, crossings, and halving lines of geometric drawings of Kn. Discrete and Computational Geometry 48 (2012), no. 1, 192-215.
• B. M. Ábrego, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, V. Sacristán, M. Saumell. On crossing numbers of geometric proximity graphs. Computational Geometry 44 (2011), 216-233.
• B. M. Ábrego, S. Fernández-Merchant, D. B. Roberts. On the maximum number of isosceles right triangles in a finite point set. Involve 4 (2011), no. 1, 27–42.
• B. M. Ábrego, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, H. Meijer, V. Sacristán, M. Saumell. Proximity graphs inside large weighted graphs (extended abstract), Proceedings of the 26th European Workshop on Computational Geometry (EuroCG'10), Dortmund, Germany, March 22-24 (2010) 9-12.
• B. M. Ábrego and S. Fernández-Merchant. Point-sets with many similar copies of a pattern: without a fixed number of collinear points or in parallelogram-free position. Geombinatorics 19 (2010), no. 4, 133-145.
• B. M. Ábrego and S. Fernández-Merchant. Point-sets in general position with many similar copies of a pattern. Geombinatorics 19 (2010), no. 3, 81-99.
• B. M. Ábrego, M. Cetina, S. Fernández-Merchant, J. Leaños, and G. Salazar. 3-symmetric and 3-decomposable drawings of Kn. Discrete Applied Mathematics 158 (2010), no. 12, 1240-1258.
• B. M. Ábrego, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, V. Sacristán, M. Saumell. On crossings in geometric proximity graphs. Proceedings of XIII Encuentros de Geometría Computacional, Universidad de Zaragoza, Spain, June 29-July 1, (2009) 151-156.
• B. M. Ábrego, E. Arkin, S. Fernández-Merchant, F. Hurtado, M. Kano, J. Mitchell, J. Urrutia. Matching points with squares. Discrete and Computational Geometry 41 (2009), 77-95.
• B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. Sum of squares of degrees in a graph. Journal of Inequalities in Pure and Applied Mathematics, 10 (2009), no. 3, Art. 64, 34 pp.
• B. M. Ábrego, S. Fernández-Merchant, and B. Llano. On the maximum number of translates in a point set. Discrete and Computational Geometry 43 (2010), 1-20.
• B. M. Ábrego, S. Fernández-Merchant, J. Leaños, and G. Salazar. A central approach to bound the number of crossings in a generalized configuration. Electronic Notes in Discrete Mathematics 30 (2008) 273-278.
• B. M. Ábrego, S. Fernández-Merchant, J. Leaños, and G. Salazar. The maximum number of halving lines and the rectilinear crossing number of Kn for n<=27. Electronic Notes in Discrete Mathematics 30 (2008) 261-266.
• B. M. Ábrego, J. Balogh, S. Fernández-Merchant, J. Leaños, and G. Salazar. An extended lower bound on the number of (<=k)-edges to generalized configurations of points and the pseudolinear crossing number of Kn. Journal of Combinatorial Theory, Series A. 115 (2008), 1257-1264.
• B. M. Ábrego, S. Fernández-Merchant, J. Leaños, and G. Salazar. Recent developments on the number of (<=k)-sets, halving-lines, and the rectilinear crossing number of Kn. Proceedings of XII Encuentros de Geometría Computacional, Universidad de Valladolid, Spain, June 25-27, (2007), ISBN 978-84-690-6900-4.
• B. M. Ábrego and S. Fernández-Merchant. Geometric drawings of Kn with few crossings. Journal of Combinatorial Theory, Series A 114 (2007) 373-379.
• B. M. Ábrego, J. Balogh, S. Fernández-Merchant, J. Leaños, and G. Salazar. On (<=k)–pseudoedges in generalized configurations and the pseudolinear crossing number of Kn. Preprint (2006).
• B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. Trace-minimal graphs and D-optimal weighing designs, Linear Algebra and its Applications 412 (2006), 161-221.
• B. M. Ábrego and S. Fernández-Merchant. A lower bound for the rectilinear crossing number. Graphs and Combinatorics, Springer-Verlag Tokyo Inc., 21 (2005), no. 3, 293 - 300.
• B. M. Ábrego, E. Arkin, S. Fernández-Merchant, F. Hurtado, M. Kano, J. Mitchell, J. Urrutia. Matching points with circles and squares. Discrete and computational geometry, 1-15, Lecture Notes in Comput. Sci., 3742, Springer, Berlin, 2005. ISBN: 3-540-30467-3.
• B. M. Ábrego, S. Fernández-Merchant, and Gy. Elekes. Structural results for planar sets with many similar subsets. Combinatorica 24 (2004), no. 4, 541-554.
• B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. D-optimal weighing designs for n=-1 (mod 4) objects and a large number of weighings, Linear Algebra and its Applications 374 (2003), 175-218.
• B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. Maximum volume simplices and trace-minimal graphs, Proceedings of X Encuentros de Geometria Computacional, University of Sevilla, Sevilla Spain, June 16-17, (2003), 51-56.
• B. M. Ábrego and S. Fernández-Merchant. The unit distance problem for centrally symmetric convex polygons. Discrete and computational geometry and graph drawing (Columbia, SC, 2001). Discrete and Computational Geometry 28 (2002), no. 4, 467-473.
• B. M. Ábrego and S. Fernández-Merchant. Convex Polyhedra in R^3 Spanning W(n^(4/3)) Congruent Triangles, Journal of Combinatorial Theory, Series A 98 (2002), 406-409.
• B. M. Ábrego and S. Fernández-Merchant. On the Maximum Number of Equilateral Triangles II. DIMACS Technical Report (1999), 99-47.
• B. M. Ábrego and S. Fernández-Merchant. On the Maximum Number of Equilateral Triangles I. Discrete and Computational Geometry 23 (2000), no. 1, 129-115.
• B. M. Ábrego, J. L. Arocha, S. Fernández-Merchant, and V. Neumann-Lara. Tightness Problems in the Plane. Discrete Mathematics 194 (1999), no. 1-3, 1-11.